Question

Thực hiện phép tính
\(\frac{4-x}{x^3+2x}\)\(-\)\(\frac{x+5}{x^3-x^2+2x-2}\)

Answer 1

\(\frac{4-x}{x^3+2x}-\frac{x+5}{x^3-x^2+2x-2}\)( ĐKXĐ : \(x\ne1\))

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

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

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

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

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

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

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

Answer 2

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

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

Đang đánh máy thì bấm gửi -..-

Answer 3

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

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

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