Question

помогите . алгебраические дроби

Answer 1

1.
$frac{3a-9}{b+2}* frac{3b+6}{18a-54}= frac{3(a-3)}{b+2}* frac{3(b+2)}{18(a-3)}= frac{1}{2} \ \ frac{ (a-2)^{2} }{b+5} : frac{3a-6}{2b+10}= frac{(a-2)(a-2)}{b+5}* frac{2(b+5)}{3(a-2)}= frac{2(a-2)}{3} \ \ frac{2x}{5x-10}- frac{x}{x-2}= frac{2x}{5(x-2)} - frac{x}{x-2}= frac{2x-5x}{5(x-2)} =- frac{3x}{5x-10}$

2.
$frac{15b}{5-b} + frac{6b}{b^{2} -25} * frac{7b+35}{3}= frac{15b}{5-b} + frac{6b}{(b-5)(b+5)}* frac{7(b+5)}{3}= frac{15b}{5-b}+ frac{14b}{b-5}= \ frac{15b}{5-b}- frac{14b}{5-b} = frac{b}{5-b}$

3.
$frac{4}{ x^{2} +4x+4}:( frac{ x^{2} +12}{ x^{2} -4} - frac{x+2}{x-2})= frac{4}{(x+2)(x+2)}:( frac{ x^{2} +12}{(x-2)(x+2)}- frac{x+2}{x-2})= \ frac{4}{(x+2)(x+2)}:( frac{ x^{2} +12-(x+2)(x+2)}{(x-2)(x+2)})= frac{4}{(x+2)(x+2)} * frac{(x-2)(x+2)}{8-4x}= \ frac{4}{4(2-x)}= frac{1}{2-x}$

при  х=1
1/(2-1)=1/1=1