Question

1/ \(\dfrac{3}{X}+\dfrac{2}{X+2}+\dfrac{2-X}{X^2+2X}\)

2/ \(\dfrac{6X}{X^2-9}+\dfrac{5X}{X-3}+\dfrac{X}{X+3}\)

CÁC BẠN CỐ GIÚP MÌNH NGHEN. CẢM ƠN CÁC BẠN.

Answer 1

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

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

\(=\dfrac{3x+6+2x+2-x}{x\left(x+2\right)}\)

\(=\dfrac{4x+8}{x\left(x+2\right)}\)

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

\(=\dfrac{4}{x}\)

Answer 2

2) \(\dfrac{6x}{x^2-9}+\dfrac{5x}{x-3}+\dfrac{x}{x+3}\)

\(=\dfrac{6x}{\left(x-3\right)\left(x+3\right)}+\dfrac{5x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{6x+5x^2+15x+x^2-3x}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{6x^2+18x}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{6x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{6x}{x-3}\)