Question

[Vũ Thảo Anh]

Thực hiện phép tính,rút gọn bt.các cậu giúp mk với

Answer 1

[Nguyễn Lê Phước Thịnh]

5) Ta có: \(\dfrac{x^3-x^2-2x-20}{x^2-4}-\dfrac{5}{x+2}+\dfrac{3}{x-2}\)

\(=\dfrac{x^3-x^2-2x-20}{\left(x-2\right)\left(x+2\right)}-\dfrac{5\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\dfrac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{x^3-x^2-2x-20-5x+10+3x+6}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{x^3-x^2-4x-4}{\left(x-2\right)\left(x+2\right)}\)

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

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

\(=x-1\)

6) Ta có: \(\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)

\(=\dfrac{x-1}{x^3}-\dfrac{x+1}{x^2\left(x-1\right)}+\dfrac{3}{x\left(x-1\right)^2}\)

\(=\dfrac{\left(x-1\right)^3}{x^3\cdot\left(x-1\right)^2}-\dfrac{x\left(x+1\right)\left(x-1\right)}{x^3\cdot\left(x-1\right)^2}+\dfrac{3x^2}{x^3\cdot\left(x-1\right)^2}\)

\(=\dfrac{x^3-3x^2+3x-1-x\left(x^2-1\right)+3x^2}{x^3\cdot\left(x-1\right)^2}\)

\(=\dfrac{x^3+3x-1-x^3+x}{x^3\cdot\left(x-1\right)^2}\)

\(=\dfrac{4x-1}{x^3\cdot\left(x-1\right)^2}\)

Answer 2

[Vũ Thảo Anh]

cảm ơn