Biểu thức P = $\frac{x-1}{2-x}:\frac{x-1}{x+2}.\frac{x-2}{4-x^2}$ có kết quả rút gọn là:

Ta có

+) $\frac{5x^2-20y^2}{3x+6y}:\frac{5x-10y}{9x}$ = $\frac{5(x^2-4y^2)}{3(x+2y)}.\frac{9x}{5(x-2y)}=\frac{5(x-2y)(x+2y).9x}{3(x+2y)5(x-2y)}$  = 3x nên A sai.

+) $\frac{45x-90y}{3x+6y}:\frac{x^2-4y^2}{x^2+4xy+4y^2}$

=$\frac{45(x-2y)}{3(x+2y)}.\frac{{(x+2y)}^2}{(x-2y)(x+2y)}=\frac{45(x-2y){(x+2y)}^2}{3{(x+2y)}^2(x-2y)}$=15

nên B sai.

+) $\frac{x^2-y^2}{2y}:(y-x)$ = $\frac{(x-y)(x+y)}{2y}.\frac{1}{y-x}=\frac{(x-y)(x+y)}{2y}.\frac{-1}{x-y}=\frac{-x-y}{2y}$ nên C sai

Đáp án cần chọn là: D

Ta có

+) $\frac{{(x-y)}^2}{{(x+y)}^2}:\frac{{(x-y)}^4}{{(x+y)}^3}$ = $\frac{{(x-y)}^2}{{(x+y)}^2}.\frac{{(x+y)}^3}{{(x-y)}^4}=\frac{x+y}{{(x-y)}^2}$ nên A đúng

+) $\frac{{(x-y)}^2}{{(x+y)}^2}:\frac{{(x-y)}^3}{{(x+y)}^3}$ = $\frac{{(x-y)}^2}{{(x+y)}^2}.\frac{{(x+y)}^3}{{(x-y)}^3}=\frac{x+y}{x-y}$ nên B sai

+) $\frac{x-y}{{(x+y)}^2}:\frac{{(x-y)}^4}{{(x+y)}^3}$ = $\frac{x-y}{{(x+y)}^2}.\frac{{(x+y)}^3}{{(x-y)}^4}=\frac{x+y}{{(x-y)}^3}$ nên C sai

+) $\frac{-{(x-y)}^2}{{(x+y)}^2}:\frac{{(x-y)}^4}{{(x+y)}^3}$ = $\frac{-{(x-y)}^2}{{(x+y)}^2}.\frac{{(x+y)}^3}{{(x-y)}^4}=\frac{-(x+y)}{{(x-y)}^2}$ nên D sai

Đáp án cần chọn là: A