Giải bài 6.21 trang 19

Đề bài

Thực hiện các phép tính sau:

a) $\frac{5-3x}{x+1}-\frac{-2+5x}{x+1}$

b) $\frac{x}{x-y}-\frac{y}{x+y}$

c) $\frac{3}{x+1}-\frac{2+3x}{x^3+1}$

Lời giải chi tiết

a) $\frac{5-3x}{x+1}-\frac{-2+5x}{x+1}$ $=\frac{5-3x-\left(-2+5x\right)}{x+1}$ $=\frac{5-3x+2-5x}{x+1}$ $=\frac{7-8x}{x+1}$

b) $\frac{x}{x-y}-\frac{y}{x+y}$ $=\frac{x\left(x+y\right)-y\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}$ $=\frac{x^2+xy-xy+y^2}{\left(x-y\right)\left(x+y\right)}$ $=\frac{x^2+y^2}{\left(x-y\right)\left(x+y\right)}$

c) $\frac{3}{x+1}-\frac{2+3x}{x^3+1}$ $=\frac{3}{x+1}-\frac{2+3x}{\left(x+1\right)\left(x^2-x+1\right)}$ $=\frac{3\left(x^2-x+1\right)-2-3x}{\left(x+1\right)\left(x^2-x+1\right)}$ $=\frac{3x^2-3x+3-2-3x}{\left(x+1\right)\left(x^2-x+1\right)}$ $=\frac{3x^2-6x+1}{\left(x+1\right)\left(x^2-x+1\right)}$