Question

упростите выражение!*

Answer 1

$( frac{x+2}{x^2+2x+4}- frac{6x-13}{x^3-8})cdot frac{2x^2+4x+8}{3-x}\\ 1) frac{x+2}{x^2+2x+4}- frac{6x-13}{x^3-8}= frac{x+2}{x^2+2x+4}- frac{6x-13}{(x-2)(x^2+2x+4)}= frac{x^2-6x+9}{(x-2)(x^2+2x+4)}=\\= frac{(x-3)^2}{(x-2)(x^2+2x+4)}\\ 2) frac{2x^2+4x+8}{3-x}cdot frac{(x-3)^2}{(x-2)(x^2+2x+4)}= frac{2(x^2+2x+4)(3-x)}{(x-2)(x^2+2x+4)} = frac{2(3-x)}{x-2}$


$frac{2ab+4b-3a-6}{2b^2+2b}:( frac{4b^2+21}{2b+2}-6 ) \\ 1) frac{4b^2+21}{2b+2}-6= frac{4b^2+21-12b-12}{2(b+1)}= frac{4b^2-12b+9}{2(b+1)}= frac{(2b-3)^2}{2(b+1)}\\ 2) frac{2ab+4b-3a-6}{2b^2+2b}: frac{(2b-3)^2}{2(b+1)}= frac{(2b-3)(a+2)}{2b(b+1)}cdot frac{2(b+1)}{(2b-3)^2}= frac{a+2}{b(2b-3)}$