Question

[Vũ Trà My]

Thực hiện các phép tính:

a) \(\dfrac{x+3}{x^2-1}-\dfrac{1}{x^2+x}\) c) \(\dfrac{3-3x}{\left(1+x\right)^2}:\dfrac{6x^2-6}{x+1}\)

b) \(\dfrac{24y^5}{7x^2}.\left(-\dfrac{21x}{12y^3}\right)\) d) \(\dfrac{7x+2}{6x-3y}:\dfrac{14x+4}{12x^2-6xy}\)

P/S: Mọi người giúp mk nha. Mk đang cần gấp lắm!!! Ai nhanh nhất mk tích!!!

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(=\dfrac{x+3}{\left(x-1\right)\left(x+1\right)}-\dfrac{1}{x\left(x+1\right)}\)

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

b: \(=\dfrac{24y^5}{7x^2}\cdot\dfrac{-21x}{12y^3}=2y^2\cdot\dfrac{-3}{x}=\dfrac{-6y^2}{x}\)

c: \(=\dfrac{-3\left(x-1\right)}{\left(x+1\right)^2}\cdot\dfrac{x+1}{6\left(x-1\right)\left(x+1\right)}=\dfrac{-1}{2\left(x+1\right)}\)

d: \(=\dfrac{7x+2}{3\left(2x-y\right)}\cdot\dfrac{6x\left(2x-y\right)}{2\left(7x+2\right)}=x\)