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12 tháng 7 2020

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12 tháng 7 2020

\(x^2-4x+\frac{1}{x+1}+2=-x^2-5x+\frac{1}{2x+1}\left(ĐK:x\ne-1;-\frac{1}{2}\right)\)

\(< =>x^2-4x+\frac{1}{x+1}+2+x^2+5x-\frac{1}{2x+1}=0\)

\(< =>2x^2+x+\frac{2x+3}{x+1}-\frac{1}{2x+1}=0\)

\(< =>2x^2+x=\frac{1}{2x+1}-\frac{2x+3}{x+1}\)

\(< =>2x^2+x=\frac{x+1-\left(2x+1\right)\left(2x+1\right)+4x+2}{\left(x+1\right)\left(x+1\right)+x^2+x}\)

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

\(< =>2x^2+x=\frac{x-4x^2+2}{2x^2+3x+1}\)

\(< =>\left(2x^2+x\right)^2+\left(2x+1\right)^2x=x-4x^2+2\)

\(< =>4x^4+8x^3+9x^2-2=0\)

nhờ bạn nào đó giải giúp ạ

2 tháng 8 2017

ĐK \(x\ne\left\{-1;-\frac{1}{2}\right\}\)

Phương trình \(\Leftrightarrow\frac{x^2-4x+1}{x+1}+1=\frac{-x^2+5x-1}{2x+1}-1\)\(\Leftrightarrow\frac{x^2-4x+1+x+1}{x+1}=\frac{-x^2+5x-1-2x-1}{2x+1}\)

\(\Leftrightarrow\frac{x^2-3x+2}{x+1}=\frac{-\left(x^2-3x+2\right)}{2x+1}\Leftrightarrow\left(x^2-3x+2\right)\left[\frac{1}{x+1}+\frac{1}{2x+1}\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2-3x+2=0\\\frac{1}{x+1}+\frac{1}{2x+1}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}\left(x-1\right)\left(x-2\right)=0\\\frac{3x+2}{\left(x+1\right)\left(2x+1\right)}=0\end{cases}}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=1;x=2\\3x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1;x=2\\x=-\frac{2}{3}\end{cases}}\left(tm\right)}\)

Vậy hệ có 3 nghiệm \(x=1;x=2;x=-\frac{2}{3}\)

3 tháng 3 2019

\(\Leftrightarrow\frac{x^2-4x+1}{x+1}+1=-\frac{x^2-5x+1}{2x+1}-1.DKXD:x\ne-1;x\ne-\frac{1}{2}\)

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

\(\Leftrightarrow\frac{x^2-3x+2}{x+1}+\frac{x^2-3x+2}{2x+1}=0\)

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

\(\Leftrightarrow\left(x^2-x-2x+2\right)\left[\frac{3x+2}{\left(x+1\right)\left(2x+1\right)}\right]=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left[\frac{3x+2}{\left(x+1\right)\left(2x+1\right)}\right]=0\)

\(\Leftrightarrow x-1=0\Leftrightarrow x=1\left(n\right)\)

\(hay:x-2=0\Leftrightarrow x=2\left(n\right)\)

\(hay:\frac{3x+2}{\left(x+1\right)\left(2x+1\right)}=0\Leftrightarrow3x+2=0\Leftrightarrow x=-\frac{2}{3}\left(n\right)\)

\(V...S=\left\{1:2:-\frac{2}{3}\right\}\)

16 tháng 2 2020

Sửa đề +2 thành +1

16 tháng 2 2020

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

9 tháng 2 2018

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

\(\Leftrightarrow\frac{\left(x^2-4x+1\right)\left(2x+1\right)+2\left(x+1\right)\left(2x+1\right)}{\left(x+1\right)\left(2x+1\right)}=\frac{\left(x^2-5x+1\right)\left(x+1\right)}{\left(2x+1\right)\left(x+1\right)}\)

\(\Leftrightarrow\frac{2x^3+x^2-8x^2-4x+2x+1+2\left(2x^2+x+2x+1\right)}{\left(x+1\right)\left(2x+1\right)}=\frac{x^3+x^2-5x^2-5x+x+1}{\left(2x+1\right)\left(x+1\right)}\)

\(\Rightarrow2x^3-7x^2-2x+1+4x^2+2x+4x+2=x^3-4x^2-4x+1\)

\(\Leftrightarrow2x^3-3x^2+4x+3-x^3+4x^2+4x-1=0\)

\(\Leftrightarrow x^3+x^2+8x-2=0\)

26 tháng 2 2022

hic, mk chx học