\(x^2+7x+13=x^2+2.x.\frac{7}{2}+\frac{49}{4}-\frac{49}{4}+13\)

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3) \(\frac{x-2}{x-5}-\frac{5}{x^2-5x}=\frac{1}{x}\) \(\Leftrightarrow\frac{x-2}{x-5}-\frac{5}{x.\left(x-5\right)}=\frac{1}{x}\) \(\Leftrightarrow\frac{x.\left(x-2\right)}{x.\left(x-5\right)}-\frac{5}{x.\left(x-5\right)}=\frac{1.\left(x-5\right)}{x.\left(x-5\right)}\) Mc: \(x.\left(x-5\right)\) \(\Leftrightarrow\) \(x^2\) - 2\(x\) - 5 = \(x\) - 5 \(\Leftrightarrow\) \(x^2\) - 2\(x\) - \(x\) - 5 + 5 = 0 \(\Leftrightarrow\) \(x^2\) - 3\(x\) = 0 \(\Leftrightarrow\) \(x\) . (\(x\) - 3) =...
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3) \(\frac{x-2}{x-5}-\frac{5}{x^2-5x}=\frac{1}{x}\)

\(\Leftrightarrow\frac{x-2}{x-5}-\frac{5}{x.\left(x-5\right)}=\frac{1}{x}\)

\(\Leftrightarrow\frac{x.\left(x-2\right)}{x.\left(x-5\right)}-\frac{5}{x.\left(x-5\right)}=\frac{1.\left(x-5\right)}{x.\left(x-5\right)}\)

Mc: \(x.\left(x-5\right)\)

\(\Leftrightarrow\) \(x^2\) - 2\(x\) - 5 = \(x\) - 5

\(\Leftrightarrow\) \(x^2\) - 2\(x\) - \(x\) - 5 + 5 = 0

\(\Leftrightarrow\) \(x^2\) - 3\(x\) = 0

\(\Leftrightarrow\) \(x\) . (\(x\) - 3) = 0

\(\Leftrightarrow\) \(x\) = 0 hoặc \(x\) - 3 = 0

\(\Leftrightarrow\) \(x\) = 0 hoặc \(x\) = 3

Vậy \(x\) = 0 hoặc \(x\) = 3

\(x-5\ne0\Rightarrow x\ne5\)

\(x^2-5\ne0\Rightarrow x\ne5\)\(x\ne0\) \(\Rightarrow\left\{{}\begin{matrix}x\ne0\\x\ne5\end{matrix}\right.\)

\(x\ne0\)

Vậy S = {3}

4) \(\frac{x-4}{x+7}-\frac{1}{x}=\frac{-7}{x^2+7x}\)

\(\Leftrightarrow\frac{x-4}{x+7}-\frac{1}{x}=\frac{-7}{x.\left(x+7\right)}\)

\(\Leftrightarrow\frac{x.\left(x-4\right)}{x.\left(x+7\right)}-\frac{1.\left(x+7\right)}{x.\left(x+7\right)}=\frac{-7}{x.\left(x+7\right)}\)

Mc: \(x.\left(x+7\right)\)

\(\Leftrightarrow x^2-4x-x-7=-7\)

\(\Leftrightarrow x^2-4x-x=-7+7\)

\(\Leftrightarrow\) \(x^2-5x=0\)

\(\Leftrightarrow x.\left(x-5\right)=0\)

\(\Leftrightarrow x=0\) hoặc \(x-5=0\)

\(\Leftrightarrow x=0\) hoặc \(x=5\)

Vậy \(x=0\) hoặc \(x=5\)

\(x+7\ne0\Rightarrow x\ne-7\)

\(x^2+7\ne0\Rightarrow x\ne-7\)\(x\ne0\) \(\Rightarrow\left\{{}\begin{matrix}x\ne0\\x\ne-7\end{matrix}\right.\)

\(x\ne0\)

Vậy S = {5}

5) \(\frac{x+2}{x-2}+\frac{x-2}{x+2}=\frac{8x}{x^2-4}\)

\(\left\{{}\begin{matrix}x-2\ne0\\x+2\ne0\\x^2-4\ne0\end{matrix}\right.\Rightarrow TXĐ\left\{{}\begin{matrix}x\ne2\\x\ne-2\end{matrix}\right.\)

Mc : \(\left(x-2\right).\left(x+2\right)\)

\(\Leftrightarrow\frac{\left(x+2\right).\left(x+2\right)}{\left(x-2\right).\left(x+2\right)}+\frac{\left(x-2\right).\left(x-2\right)}{\left(x+2\right).\left(x-2\right)}=\frac{8x}{\left(x-2\right).\left(x+2\right)}\)

\(\Leftrightarrow x^2+2x+2x+4+x^2-2x-2x+4=8x\)

\(\Leftrightarrow x^2+x^2+2x+2x-2x-2x-8x+4+4=0\)

\(\Leftrightarrow2x^2-8x+8=0\)

\(\Leftrightarrow\) \(2x^2-4x-4x+8=0\)

\(\Leftrightarrow\) \(2x.\left(x-2\right)-4.\left(x-2\right)=0\)

\(\Leftrightarrow\left(2x-4\right).\left(x-2\right)=0\)

\(\Leftrightarrow2x-4=0\) hoặc \(x-2=0\)

\(\Leftrightarrow x=2\) hoặc \(x=2\)

\(\Leftrightarrow x=2\) (Loại) hoặc x = 2 (Loại)

Vậy S = \(\left\{\varnothing\right\}\)

6) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)

\(\Leftrightarrow\frac{\left(x+1\right).\left(x+1\right)}{\left(x-1\right).\left(x+1\right)}-\frac{\left(x-1\right).\left(x-1\right)}{\left(x+1\right).\left(x-1\right)}=\frac{4}{\left(x-1\right).\left(x+1\right)}\)

MC: \(\left(x-1\right).\left(x+1\right)\)

\(\Leftrightarrow x^2+x+x+1-x^2+x+x-1=4\)

\(\Leftrightarrow x^2-x^2+x+x+x+x+1-1-4=0\)

\(\Leftrightarrow4x-4=0\)

\(\Leftrightarrow4.\left(x-1\right)=0\)

\(\Leftrightarrow\) 4 = 0 hoặc \(x-1=0\)

\(\Leftrightarrow\) 4 = 0 hoặc \(x=1\)

\(\Leftrightarrow\) 4 = 0 (Loại) hoặc \(x=1\) (Loại)

Vậy S = \(\left\{\varnothing\right\}\)

7) \(\frac{x+1}{x-1}+\frac{-4x}{x^2-1}=\frac{x-1}{x+1}\)

\(\Leftrightarrow\frac{\left(x+1\right).\left(x+1\right)}{\left(x-1\right).\left(x+1\right)}+\frac{-4x}{\left(x-1\right).\left(x+1\right)}=\frac{\left(x-1\right).\left(x-1\right)}{\left(x+1\right).\left(x-1\right)}\)

\(Mc:\left(x-1\right).\left(x+1\right)\)

\(\Leftrightarrow\) \(x^2+x+x+1-4x=x^2-x-x+1\)

\(\Leftrightarrow x^2-x^2+x+x-4x+x+x=-1+1\)

\(\Leftrightarrow0=0\) (Nhận)

Vậy S = \(\left\{x\in R;x\ne\pm1\right\}\)

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8 tháng 1 2020

1.

\(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)

\(MC:12\)

Quy đồng :

\(\Rightarrow\frac{3.\left(2x+3\right)}{12}-\left(\frac{2.\left(5x+3\right)}{12}\right)=\frac{3x-4}{12}\)

\(\frac{6x+9}{12}-\left(\frac{10x+6}{12}\right)=\frac{3x-4}{12}\)

\(\Leftrightarrow6x+9-\left(10x+6\right)=3x-4\)

\(\Leftrightarrow6x+9-3x=-4-9+16\)

\(\Leftrightarrow-7x=3\)

\(\Leftrightarrow x=\frac{-3}{7}\)

2.\(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)

\(MC:20\)

Quy đồng :

\(\frac{15.\left(2x+1\right)}{20}-\frac{20}{20}=\frac{2.\left(15x-1\right)}{20}\)

\(\Leftrightarrow15\left(2x+1\right)-20=2\left(15x-1\right)\)

\(\Leftrightarrow30x+15-20=15x-2\)

\(\Leftrightarrow15x=3\)

\(\Leftrightarrow x=\frac{3}{15}=\frac{1}{5}\)

27 tháng 11 2019

ơ bài nào v ...................

27 tháng 11 2019

Cho 2 số a,b thỏa mãn \(a^3+b^3+3\left(a^2+b^2\right)+4\left(a+b\right)+4=0\)

Tính giá trị của biểu thức \(M=2018\left(a+b\right)^2\)

26 tháng 3 2020

a)

\(\frac{x}{3}-\frac{5x}{6}-\frac{15x}{12}=\frac{x}{4}-5\)

\(\Leftrightarrow\frac{4x-10x-15x}{12}=\frac{3x-60}{12}\)

\(\Leftrightarrow\frac{-10x-11}{12}=\frac{3x-60}{12}\)

\(\Leftrightarrow\frac{-10x-11-3x+60}{12}=0\)

\(\Leftrightarrow\frac{49-13x}{12}=0\)

\(\Rightarrow49-13x=0\)

\(\Rightarrow x=\frac{-49}{13}\)

26 tháng 3 2020

b)

\(\frac{8x-3}{4}-\frac{3x-2}{2}=\frac{2x-1}{2}+\frac{x+3}{4}\)

\(\Leftrightarrow\frac{8x-3-6x+4}{4}=\frac{4x-2+x+3}{4}\)

\(\Leftrightarrow\frac{2x+1}{4}=\frac{5x+1}{4}\)

\(\Leftrightarrow\frac{2x+1-5x-1}{4}=0\)

\(\Leftrightarrow\frac{-3x}{4}=0\)

\(\Rightarrow-3x=0\)

\(\Rightarrow x=0\)

20 tháng 3 2020

\( a)\dfrac{{x - 3}}{5} = 6 - \dfrac{{1 - 2x}}{2}\\ \Leftrightarrow 2\left( {x - 3} \right) = 60 - 5\left( {1 - 2x} \right)\\ \Leftrightarrow 2x - 6 = 60 - 5 + 10x\\ \Leftrightarrow 8x = - 61\\ \Leftrightarrow x = - \dfrac{{61}}{8}\\ b)\dfrac{{3x - 2}}{6} - 5 = \dfrac{{3 - 2\left( {x + 7} \right)}}{4}\\ \Leftrightarrow 2\left( {3x - 2} \right) - 60 = 3\left( { - 11 - 2x} \right)\\ \Leftrightarrow 6x - 4 - 60 = - 33 - 6x\\ \Leftrightarrow 12x = 31\\ \Leftrightarrow x = \dfrac{{31}}{{12}} \)

20 tháng 3 2020

\(a.\frac{x-3}{5}=6-\frac{1-2x}{2}\\\Leftrightarrow \frac{2\left(x-3\right)}{10}=\frac{60}{10}-\frac{5\left(1-2x\right)}{10}\\ \Leftrightarrow2\left(x-3\right)=60-5\left(1-2x\right)\\\Leftrightarrow 2x-6=60-5+10x\\\Leftrightarrow 2x-10x=6+60-5\\\Leftrightarrow -8x=61\\ \Leftrightarrow x=-\frac{61}{8}\)

Vậy nghiệm của phương trình trên là \(-\frac{61}{8}\)

3) \(\frac{x-2}{x-5}\) \(-\frac{5}{x^2-5x}=\frac{1}{x}\) \(\Leftrightarrow\) \(\frac{x-2}{x-5}-\frac{5}{x.\left(x-5\right)}=\frac{1}{x}\) \(\Leftrightarrow\frac{\left(x-2\right).\left(x+5\right)}{x.\left(x-5\right)}-\frac{5}{x.\left(x-5\right)}=\frac{1.\left(x+5\right)}{x.\left(x-5\right)}\) \(\Leftrightarrow x^2+5x-2x-10-5=1x+5\) \(\Leftrightarrow x^2+5x-2x-1x-10-5-5\) = 0 \(\Leftrightarrow\) \(x^2+2x-20=0\) \(\Leftrightarrow x^2+2x-10x-20=0\) \(\Leftrightarrow\) (x\(^2\) + 2x) - (10x +...
Đọc tiếp

3) \(\frac{x-2}{x-5}\) \(-\frac{5}{x^2-5x}=\frac{1}{x}\)

\(\Leftrightarrow\) \(\frac{x-2}{x-5}-\frac{5}{x.\left(x-5\right)}=\frac{1}{x}\)

\(\Leftrightarrow\frac{\left(x-2\right).\left(x+5\right)}{x.\left(x-5\right)}-\frac{5}{x.\left(x-5\right)}=\frac{1.\left(x+5\right)}{x.\left(x-5\right)}\)

\(\Leftrightarrow x^2+5x-2x-10-5=1x+5\)

\(\Leftrightarrow x^2+5x-2x-1x-10-5-5\) = 0

\(\Leftrightarrow\) \(x^2+2x-20=0\)

\(\Leftrightarrow x^2+2x-10x-20=0\)

\(\Leftrightarrow\) (x\(^2\) + 2x) - (10x + 20) = 0

\(\Leftrightarrow\) x.(x + 2) - 10.(x + 2) = 0

\(\Leftrightarrow\)

4) \(\frac{x-4}{x+7}-\frac{1}{x}=\frac{-7}{x^2+7x}\)

\(\Leftrightarrow\frac{x-4}{x+7}-\frac{1}{x}=\frac{-7}{x\left(x+7\right)}\)

\(\Leftrightarrow\frac{\left(x-4\right).\left(x+7\right)}{x.\left(x+7\right)}-\frac{1.\left(x+7\right)}{x.\left(x+7\right)}=\frac{-7}{x.\left(x+7\right)}\)

\(\Leftrightarrow\) \(x^2+7x-4x-28-x-7=-7\)

\(\Leftrightarrow x^2+7x-4x-x-28-7+7=0\)

\(\Leftrightarrow\) x\(^2\) + 2x - 28 = 0

\(\Leftrightarrow\) x\(^2\) + 2x - 14x - 28 = 0

\(\Leftrightarrow\) (x\(^2\) + 2x) - (14x + 28) = 0

\(\Leftrightarrow\) x.(x + 2) - 14.(x + 2) = 0

\(\Leftrightarrow\) (x - 14) = 0 hoặc (x + 2) = 0

\(\Leftrightarrow\) x = 4 (Nhận) hoặc x = -2 (Loại)

5) \(\frac{x+2}{x-2}+\frac{x-2}{x+2}=\frac{8x}{x^2-4}\)

\(\Leftrightarrow\) \(\frac{\left(x+2\right).\left(x+2\right)}{\left(x-2\right).\left(x+2\right)}+\frac{\left(x-2\right).\left(x-2\right)}{\left(x+2\right).\left(x-2\right)}=\frac{8x}{\left(x-2\right).\left(x+2\right)}\)

\(\Leftrightarrow x^2+2x+2x+4+x^2-2x-2x+4=8x\)

\(\Leftrightarrow\) \(x^2+x^2+2x+2x-2x-2x-8x+4+4=0\)

\(\Leftrightarrow2x^2-8x+8=0\)

\(\Leftrightarrow\) 2x\(^2\) - 2x - 8x + 8 = 0

\(\Leftrightarrow\) 2x(x - 1) - 8(x - 1) = 0

\(\Leftrightarrow\) 2x - 8 = 0 hoặc x - 1 = 0

\(\Leftrightarrow\) 2x = 8 hoặc x = 1

\(\Leftrightarrow\) x = 4 (Nhận) hoặc x = 1 (Nhận)

Vậy S = {4; 1}

6) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)

\(\Leftrightarrow\) \(\frac{\left(x+1\right).\left(x+1\right)}{\left(x-1\right).\left(x+1\right)}-\frac{\left(x-1\right).\left(x-1\right)}{\left(x+1\right).\left(x-1\right)}=\frac{4}{\left(x-1\right).\left(x+1\right)}\)

\(\Leftrightarrow\) x\(^2\) + x + x + 1 - x\(^2\) + x + x - 1 = 4

\(\Leftrightarrow\) 4x - 4 = 0

\(\Leftrightarrow\) 4 (x - 1) =0

\(\Leftrightarrow\) x - 1 = 0 / 4 = 0

\(\Leftrightarrow\) x = 1 (Nhận)

Vậy S = {1}

7) \(\frac{x+1}{x-1}+\frac{-4x}{x^2-1}=\frac{x-1}{x+1}\)

\(\Leftrightarrow\) \(\frac{\left(x+1\right).\left(x+1\right)}{\left(x-1\right).\left(x+1\right)}+\frac{-4x}{\left(x-1\right).\left(x+1\right)}=\frac{\left(x-1\right).\left(x-1\right)}{\left(x+1\right).\left(x+1\right)}\)

\(\Leftrightarrow x^2+x+x+1-4x=x^2-x-x+1\)

\(\Leftrightarrow\) 0

Vậy S ={\(\varnothing\)}

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