Giải Bài tập 2 trang 35 sgk Toán 8 tập 1 Chân trời

a) $\frac{1}{2a}+\frac{2}{3b}=\frac{3b}{6ab}+\frac{4a}{6ab}=\frac{3b+4a}{6ab}$

b) $\frac{x-1}{x+1}-\frac{x+1}{x-1}=\frac{(x-1)^{2}}{(x-1)(x+1)}-\frac{(x+1)^{2}}{(x-1)(x-1)}=\frac{(x-1)^{2}-(x+1)^{2}}{(x+1)(x-1)}=\frac{(x-1-x-1)(x-1+x+1)}{x-1}=\frac{-4x}{(x-1)(x+1)}$

c) $\frac{x+y}{xy}-\frac{y+z}{yz}=\frac{(x+y)z}{xyz}-\frac{(y+z)x}{xyz}=\frac{xz+yz-xy-xz}{xyz}=\frac{y(z-x)}{xyz}=\frac{z-x}{xz}$

d) $\frac{2}{x-3}-\frac{12}{x^{2}-9}=\frac{2(x+3)}{(x-3)(x-3)}-\frac{12}{(x-3)(x+3)}=\frac{2x+6-12}{(x-3)(x+3)}=\frac{2x-6}{(x+3)(x-3)}=\frac{2(x-3)}{(x-3)(x+3)}=\frac{2}{x+3}$

e) $\frac{1}{x-2}+\frac{2}{x^{2}-4x+4}=\frac{x-2}{(x-2)^{2}}+\frac{2}{(x-2)^{2}}=\frac{x-2+2}{(x-2)^{2}}=\frac{x}{(x-2)^{2}}$