Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1) \(\frac{x-1}{x-5}=\frac{6}{7};\left(x-1\right).7=\left(x-5\right).6\)
7x - 7 = 6x - 30
=> 7x - 6x = -30 - (-7)
x = -23
2) \(\frac{x-1}{3}=\frac{x+3}{5};\left(x-1\right).5=\left(x+3\right).3\)
5x - 5 = 3x + 9
=> 5x - 3x = 9 - (-5)
2x = 14
x = 7
3) \(\frac{3}{7}=\frac{2x+1}{3x+5};\left(3x+5\right).3=\left(2x+1\right).7\)
9x + 15 = 14x + 7
9x - 14x = 7-15
5x = -8
x = -8/5
1) =>\(\hept{\begin{cases}x-1=6\\x-5=7\end{cases}=>\hept{\begin{cases}x=6+1=7\\x=7+5=13\end{cases}}}\)
Vậy x\(\varepsilon\){7;13}
2)
(x - 7)x+1 - (x - 7)x+1 = 0
<=> 0 = 0
Vậy phương trình có nghiệm với mọi x thuộc R
b/ Chi cần áp dụng tính chất dãy tỷ số bằng nhau thì ra thôi
c)\(\left|2x+3\right|=x+2\)
Đk:\(x+2\ge0\Rightarrow x\ge-2\)
TH1:2x+3=x+2
\(\Rightarrow2x-x=2-3\)
\(\Rightarrow x=-1\)(Thỏa mãn đk )
TH2:2x+3=-x-2
\(\Rightarrow2x+x=-2+3\)
\(\Rightarrow3x=1\)
\(\Rightarrow x=\frac{1}{3}\)(Thỏa mãn đk)
Vậy x=-1 hoặc x=1/3
\(a,\frac{3x+2}{5x+7}=\frac{3x-1}{5x-1}=\frac{\left(3x+2\right)-\left(3x-1\right)}{\left(5x+7\right)-\left(5x-1\right)}=\frac{3}{8};\frac{3x+2}{5x+7}=\frac{3}{8}\Leftrightarrow24x+16=15x+21\Leftrightarrow9x=5\Leftrightarrow x=\frac{5}{9}\) \(b,\frac{37-x}{x+13}=\frac{3}{7}\Leftrightarrow37.7-7x=3x+39\Leftrightarrow259-7x=3x+39\Leftrightarrow220-7x=3x\Leftrightarrow10x=220\Leftrightarrow x=22\) \(c,\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}=\frac{x+4}{2x+6}=\frac{\left(x+4\right)-\left(x+1\right)}{2x+6-\left(2x+1\right)}=\frac{3}{5};\frac{x+1}{2x+1}=\frac{3}{5}\Leftrightarrow5x+5=6x+3\Leftrightarrow x=2\) \(d,\frac{x-2}{x+2}=\frac{x+3}{x-4}=\frac{\left(x+3\right)-\left(x-2\right)}{\left(x-4\right)-\left(x+2\right)}=\frac{5}{-6};\frac{x-2}{x+2}=\frac{5}{-6}\Leftrightarrow6\left(2-x\right)=5x+10\Leftrightarrow2-6x=5x\Leftrightarrow x=\frac{2}{11}\) \(f,\frac{3x-5}{x}=\frac{9x}{3x+2}=\frac{9x-15}{3x}=\frac{9x-\left(9x-15\right)}{\left(3x+2\right)-3x}=\frac{15}{2};\frac{9x}{3x+2}=\frac{15}{2}\Leftrightarrow18x=45x+30\Leftrightarrow27x+30=0\Leftrightarrow x=\frac{-10}{9}\) \(e,\frac{x+2}{6}=\frac{5x-1}{5}\Leftrightarrow5\left(x+2\right)=6\left(5x-1\right)\Leftrightarrow5x+10=30x-6\Leftrightarrow10=25x-6\Leftrightarrow25x=16\Leftrightarrow x=\frac{16}{25}\)
a)x-3/x+5=5/7 suy ra 7.(x-3) = 5(x+5)
Tương đương : 7x - 21 = 5x + 25
7x - 5x = 25 + 21 = 46
2x = 46 suy ra : x = 46/2 = 23
Vậy x = 23
a)\(\frac{x+3}{x+5}=7\Leftrightarrow x+3=7\left(x+5\right)\)
\(\Leftrightarrow x+3=7x+35\)
\(\Leftrightarrow-6x=32\)
\(\Leftrightarrow x=-\frac{16}{3}\)
b)\(\frac{2x-1}{3x+5}=-\frac{2}{3}\)
\(\Leftrightarrow3\left(2x-1\right)=-2\left(3x+5\right)\)
\(\Leftrightarrow6x-3=-6x-10\)
\(\Leftrightarrow12x=-7\)
\(\Leftrightarrow x=-\frac{7}{12}\)
c)\(\frac{x+1}{4}=\frac{9}{x+1}\Leftrightarrow\left(x+1\right)^2=36\)
\(\Leftrightarrow\left(x+1\right)^2=6^2\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=6\\x+1=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-7\end{cases}}}\)
d)\(\frac{6x-1}{2x+3}=\frac{3x}{x+2}\)
\(\Leftrightarrow\left(6x-1\right)\left(x+2\right)=3x\left(2x+3\right)\)
\(\Leftrightarrow6x^2+12x-x-2=6x^2+9x\)
\(\Leftrightarrow2x=2\Leftrightarrow x=1\)
b)
\(\frac{x-1}{x-5}=\frac{6}{7}\)
\(\Rightarrow\left(x-1\right)7=\left(x-5\right)6\)
\(\Rightarrow7x-7=6x-30\)
\(\Rightarrow7x-6x=-30+7\)
\(\Rightarrow x=-23\)
c)
\(\frac{\left(6x-5\right)}{-7}=\frac{5x-3}{-5}\)
\(\Rightarrow\left(6x-5\right)\left(-5\right)=\left(5x-3\right)\left(-7\right)\)
\(\Rightarrow25-30x=21-35x\)
\(\Rightarrow-30x+35x=21-25\)
\(\Rightarrow5x=-4\)
\(\Rightarrow x=-\frac{4}{5}\)