https://olm.vn/hoi-dap/question/1027904.html

tk nhé 

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\(P=\frac{2x^5-x^4-2x+1}{4x^2-1}+\frac{8x^2-4x+2}{ }\)

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

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

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

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

Vậy \(P=\frac{x^4+1}{2x+1}\)

Nguyễn Hồng Hà My làm gì có thế mà cũng được hác à

a. 2x

b.\({3x}\over x^2-1\)

a, \(A=\frac{4x^2\left(x-2\right)+3\left(x-2\right)}{2x\left(x-2\right)+x-2}\)

\(=\frac{\left(x-2\right)\left(4x^2+3\right)}{\left(x-2\right)\left(2x+1\right)}=\frac{4x^2+3}{2x-1}\left(ĐKXĐ:x\ne2;x\ne-\frac{1}{2}\right)\)

b, \(A\in Z\Leftrightarrow\frac{4x^2+3}{2x-1}\in Z\Leftrightarrow2x+1+\frac{4}{2x-1}\in Z\)

\(\Leftrightarrow\frac{4}{2x-1}\in Z\Leftrightarrow4⋮\left(2x-1\right)\)

\(\Rightarrow2x-1\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

Mà 2x - 1 là số lẻ nên \(2x-1\in\left\{-1;1\right\}\Rightarrow x\in\left\{0;1\right\}\) (thỏa mãn ĐKXĐ)

a) ĐKXĐ: \(x\ne\left\{-3;-\frac{1}{3}\right\}\)

Ta có: \(\frac{3x-1}{3x+1}+\frac{x-3}{x+3}=\)\(\frac{\left(3x-1\right)\left(x+3\right)+\left(x-3\right)\left(3x+1\right)}{\left(3x+1\right)\left(x+3\right)}\)=\(\frac{3x^2+9x-x-3+3x^2+x-9x-3}{3x^2+9x+x+3}\)

          =  \(\frac{6x^2-6}{3x^2+10x+3}\)

=>  \(\frac{6x^2-6}{3x^2+10x+3}=2\)

<=> \(6x^2-6=6x^2+20x+6\)

<=> 20x=12

<=>x=\(\frac{12}{20}=\frac{3}{5}\)

Vậy x=3/5