Giải bài 6.20 trang 19

Đề bài

Thực hiện các phép tính:

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

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

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

Lời giải chi tiết

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

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

c) $\frac{x}{2x-6}+\frac{9}{2x\left(3-x\right)}$ $=\frac{x}{2\left(x-3\right)}-\frac{9}{2x\left(x-3\right)}$ $=\frac{x^2}{2x\left(x-3\right)}-\frac{9}{2x\left(x-3\right)}$ $=\frac{x^2-9}{2x\left(x-3\right)}$ $=\frac{\left(x-3\right)\left(x+3\right)}{2x\left(x-3\right)}$ $=\frac{x+3}{2x}$