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\(P=\left(\frac{x-1}{x+3}+\frac{2}{x-3}+\frac{x^2+3}{9-x^2}\right):\left(\frac{2x-1}{2x+1}-1\right)\)\(\left(đkcđ:x\ne\pm3;x\ne-\frac{1}{2}\right)\)
\(=\left(\frac{\left(x-1\right).\left(x-3\right)+2.\left(x+3\right)-\left(x^2+3\right)}{x^2-9}\right):\left(\frac{2x-1-\left(2x+1\right)}{2x+1}\right)\)
\(=\frac{x^2-4x+3+2x+6-x^2-3}{x^2-9}:\frac{-2}{2x+1}\)
\(=\frac{-2x-6}{x^2-9}.\frac{2x+1}{-2}\)
\(=\frac{-2\left(x+3\right)}{\left(x-3\right).\left(x+3\right)}.\frac{2x+1}{-2}\)
\(=\frac{2x+1}{x-3}\)
b)\(\left|x+1\right|=\frac{1}{2}\Leftrightarrow\orbr{\begin{cases}x+1=\frac{1}{2}\\x+1=-\frac{1}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\left(koTMđkxđ\right)\\x=-\frac{3}{2}\left(TMđkxđ\right)\end{cases}}}\)
thay \(x=-\frac{3}{2}\) vào P tâ đc: \(P=\frac{2x+1}{x-3}=\frac{2.\left(-\frac{3}{2}\right)+1}{-\frac{3}{2}-3}=\frac{4}{9}\)
c)ta có:\(P=\frac{x}{2}\Leftrightarrow\frac{2x+1}{x-3}=\frac{x}{2}\)
\(\Rightarrow2.\left(2x+1\right)=x.\left(x-3\right)\)
\(\Leftrightarrow4x+2=x^2-3x\)
\(\Leftrightarrow x^2-7x-2=0\)
\(\Leftrightarrow x^2-2.\frac{7}{2}+\frac{49}{4}-\frac{57}{4}=0\)
\(\Leftrightarrow\left(x-\frac{7}{2}\right)^2-\frac{57}{4}=0\)
\(\Leftrightarrow\left(x-\frac{7}{2}-\frac{\sqrt{57}}{2}\right).\left(x-\frac{7}{2}+\frac{\sqrt{57}}{2}\right)\)
bạn tự giải nốt nhé!!
d)\(x\in Z;P\in Z\Leftrightarrow\frac{2x+1}{x-3}\in Z\Leftrightarrow\frac{2x-6+7}{x-3}=2+\frac{7}{x-3}\in Z\)
\(2\in Z\Rightarrow\frac{7}{x-3}\in Z\Leftrightarrow x-3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
bạn tự làm nốt nhé
a, \(\left(\dfrac{x^2-4x+3+2x+6-x^2-3}{\left(x+3\right)\left(x-3\right)}\right):\left(\dfrac{2x-1-2x-1}{2x+1}\right)\)
\(=\dfrac{-2x+6}{\left(x+3\right)\left(x-3\right)}:\dfrac{-2}{2x+1}=\dfrac{-2\left(x-3\right)\left(2x+1\right)}{-2\left(x+3\right)\left(x-3\right)}=\dfrac{2x+1}{x+3}\)
b, \(\left|x+1\right|=\dfrac{1}{2}\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}-1\\x=-\dfrac{1}{2}-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\left(ktmđk\right)\\x=-\dfrac{3}{2}\end{matrix}\right.\)
Thay x = -3/2 ta được \(\dfrac{2\left(-\dfrac{3}{2}\right)+1}{-\dfrac{3}{2}+3}=\dfrac{-2}{\dfrac{3}{2}}=-\dfrac{4}{3}\)
Ta có: \(M-N=77^2+75^2+....+1^2-\left(76^2+74^2+...+2^2\right)\)
\(=77^2+75^2+....+1^2-76^2-74^2-...-2^2\)
\(=\left(77^2-76^2\right)+\left(75^2-74^2\right)+...+\left(3^2-2^2\right)+1^2\)
\(=\left(77-76\right)\left(77+76\right)+\left(75-74\right)\left(75+74\right)+...+\left(3-2\right)\left(3+2\right)+1\)
\(=77+76+75+74+...+3+2+1\)
\(=\frac{\left[\left(77-1\right):1+1\right].\left(1+77\right)}{2}=\frac{77.78}{2}=3003\)
Thay vào S, ta có: \(S=\frac{M-N-3}{3000}=\frac{3003-3}{3000}=\frac{3000}{3000}=1\)
a, ĐKXĐ : \(x-1\ne0\)
=> \(x\ne1\)
TH1 : \(x-2\ge0\left(x\ge2\right)\)
=> \(\left|x-2\right|=x-2=1\)
=> \(x=3\left(TM\right)\)
- Thay x = 3 vào biểu thức P ta được :
\(P=\frac{3+2}{3-1}=\frac{5}{2}\)
TH2 : \(x-2< 0\left(x< 2\right)\)
=> \(\left|x-2\right|=2-x=1\)
=> \(x=1\left(KTM\right)\)
Vậy giá trị của P là \(\frac{5}{2}\) .
a) \(P=\frac{x+2}{x-1}\) \(\left(ĐKXĐ:x\ne1\right)\)
Ta có: \(\left|x-2\right|=1\text{⇔}\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\text{⇔}\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\) (loại x = 1 vì x ≠ 1)
Thay \(x=3\) vào P, ta có:
\(P=\frac{3+2}{3-2}=\frac{5}{1}=5\)
Vậy P = 5 tại x = 3.
b) \(Q=\frac{x-1}{x}+\frac{2x+1}{x^2+x}=\frac{x-1}{x}+\frac{2x+1}{x\left(x+1\right)}=\frac{x^2-1}{x\left(x+1\right)}+\frac{2x+1}{x\left(x+1\right)}\) (ĐKXĐ: x ≠ 0, x ≠ -1)
\(=\frac{x^2+2x}{x\left(x+1\right)}=\frac{x\left(x+2\right)}{x\left(x+1\right)}=\frac{x+2}{x+1}\)
\(B-A=76^2+74^2+...+4^2+2^2-77^2-...-3^2-1^2\)
\(=-77^2+\left(76^2-75^2\right)+\left(74^2-73^2\right)+...+\left(2^2-1^2\right)\)
\(=-77^2+\left(76+75\right)+\left(74+73\right)+...+\left(2+1\right)\)
\(=-77^2+\frac{\left(76+1\right)\left[\left(76-1\right)+1\right]}{2}=-77^2+2926\)
\(\Rightarrow A-B=77^2-2926=5929-5926=3\)
\(\Rightarrow A-B-3=3-3=0\)
\(\Rightarrow P=\frac{0}{3000}=0\)
M-N=(77^2-76^2)+(75^2-74^2)+...+(3^2-2^2)+1(dùng HĐT số 3)
M-N=1+2+3+4+5+...+76+77
M-N=3003
Nên (M-N-3)/3=3000/3=1000
Nhớ tich cho mình nha bạn
Xét
M – N = 77 2 + 75 2 + 73 2 + … + 3 2 + 1 2 – ( 76 2 + 74 2 + … + 2 2 ) = ( 77 2 – 76 2 ) + ( 75 2 – 74 2 ) + ( 73 2 – 71 2 ) + … + ( 3 2 – 2 2 ) + 1 2
= (77 + 76)(77 – 76) + (75 + 74)(75 – 74) + … + (3 + 2)(3 – 2) + 1
= (77 + 76).1 + (75 + 74).1 + … + (3 + 2).1 + 1
= 77 + 76 + 75 + 74 + 73 + … + 3 + 2 + 1
= 77 + 1 2 . 77 = 3003
Từ đó M - N - 3 3000 = 3003 - 3 3000 = 3000 3000 = 1
Đáp án cần chọn là: C