A=x³/x²--4.x+2/x-x-4xx-4/xx-2

Điều kiện x \(\ne\)+-2

Ý b c tự làm 

\(A=\frac{x^3}{x^2-4}.\frac{x+2}{x}-\frac{4x-4}{x-2}\)   \(ĐKXĐ:x\ne0;x\ne2\)

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

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

\(A=\frac{\left(x-2\right)^2}{x-2}\)

\(A=x-2\)

vậy \(A=x-2\)

a)     \(ĐKXĐ:x\ne-3;x\ne2\)

b)     \(P=\frac{\left(x+2\right)\left(x-2\right)}{\left(x+3\right)\left(x-2\right)}-\frac{5}{\left(x-2\right)\left(x+3\right)}-\frac{x+3}{\left(x-2\right)\left(x+3\right)}\)

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

\(P=\frac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\)

\(P=\frac{\left(x+3\right)\left(x-4\right)}{\left(x+3\right)\left(x-2\right)}\)

vậy \(P=\frac{x-4}{x-2}\)

\(P=\frac{-3}{4}\) \(\Leftrightarrow\frac{x-4}{x-2}=\frac{-3}{4}\)

\(\Leftrightarrow4\left(x-4\right)=-3.\left(x-2\right)\)

\(\Leftrightarrow4x-16=-3x+6\)

\(\Leftrightarrow7x=22\)

\(\Leftrightarrow x=\frac{22}{7}\)

c) \(P\in Z\Leftrightarrow\frac{x-4}{x-2}\in Z\)

\(\frac{x-2-6}{x-2}=1-\frac{6}{x-2}\in Z\)

mà \(1\in Z\Rightarrow\left(x-2\right)\inƯ\left(6\right)\in\left(\pm1;\pm2;\pm3;\pm6\right)\)

mà theo ĐKXĐ:  \(\Rightarrow\in\left(\pm1;-2;3;\pm6\right)\)

thay mấy cái kia vào rồi tìm \(x\)

d) \(x^2-9=0\Rightarrow x^2=9\Rightarrow x=\pm3\)

khi \(x=3\Rightarrow P=\frac{3-4}{3-2}=-1\)

khi \(x=-3\Rightarrow P=\frac{-3-4}{-3-2}=\frac{-7}{-5}=\frac{7}{5}\)

Ta có :

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

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

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

Để A có giá trị là 1 số nguyên

\(\Leftrightarrow\frac{2}{x-1}\inℤ\)

\(\Leftrightarrow x-1\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

( thoả mãn ĐKXĐ )

Vậy ........

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

Để \(x\in Z,A\in Z\Leftrightarrow x-1\inƯ\left(2\right)\)

\(Ư\left(2\right)\in\left\{\pm1;\pm2\right\}\)

Vậy ........

a) \(x\ne2;-2;-4\)

b) và c) thì bạn rút gọn M rồi tính

cách nhân ntn ạ