Сократите дробь: 1) (9x²−4)/(3x²−13x−10); 2) (x²+4x−5)/(x³+5x²−x−5); 3) (12x−3x²)/(3x²−17x+20); 4) (x²+10x+25)/(10−3x−x²); 5) (2x−8x³)/(4x³+12x²−x−3); 6) (4x²−2x+1)/(8x³+1); 7) (8x³−27)/(12−5x−2x²); 8) (12−4x−x²)/(x²+6x−16); 9) (2x²−15x+28)/(4x²−28x+49); 10) (6x³−5x²+18x−15)/(3x+x³).

Question

Вопрос:

Фото задания: Сократите дробь: 1) (9x²−4)/(3x²−13x−10); 2) (x²+4x−5)/(x³+5x²−x−5); 3) (12x−3x²)/(3x²−17x+20); 4) (x²+10x+25)/(10−3x−x²); 5)…

Сократите дробь: 1) (9x²−4)/(3x²−13x−10); 2) (x²+4x−5)/(x³+5x²−x−5); 3) (12x−3x²)/(3x²−17x+20); 4) (x²+10x+25)/(10−3x−x²); 5) (2x−8x³)/(4x³+12x²−x−3); 6) (4x²−2x+1)/(8x³+1); 7) (8x³−27)/(12−5x−2x²); 8) (12−4x−x²)/(x²+6x−16); 9) (2x²−15x+28)/(4x²−28x+49); 10) (6x³−5x²+18x−15)/(3x+x³).

Accepted Answer

\(\frac{9x^2-4}{3x^2-13x-10}=\frac{(3x-2)(3x+2)}{(3x+2)(x-5)}=\frac{3x-2}{x-5}\).
\(\frac{x^2+4x-5}{x^3+5x^2-x-5}=\frac{(x+5)(x-1)}{(x+5)(x^2-1)}=\frac1{x+1}\).
\(\frac{12x-3x^2}{3x^2-17x+20}=\frac{-3x(x-4)}{(3x-5)(x-4)}=\frac{-3x}{3x-5}\).
\(\frac{x^2+10x+25}{10-3x-x^2}=\frac{(x+5)^2}{-(x+5)(x-2)}=-\frac{x+5}{x-2}\).
\(\frac{2x-8x^3}{4x^3+12x^2-x-3}=\frac{-2x(2x-1)(2x+1)}{(x+3)(2x+1)(2x-1)}=-\frac{2x}{x+3}\).
\(\frac{4x^2-2x+1}{8x^3+1}=\frac{4x^2-2x+1}{(2x+1)(4x^2-2x+1)}=\frac1{2x+1}\).
\(\frac{8x^3-27}{12-5x-2x^2}=\frac{(2x-3)(4x^2+6x+9)}{-(2x-3)(x+4)}=-\frac{4x^2+6x+9}{x+4}\).
\(\frac{12-4x-x^2}{x^2+6x-16}=\frac{-(x-2)(x+6)}{(x-2)(x+8)}=-\frac{x+6}{x+8}\).
\(\frac{2x^2-15x+28}{4x^2-28x+49}=\frac{(2x-7)(x-4)}{(2x-7)^2}=\frac{x-4}{2x-7}\).
\(\frac{6x^3-5x^2+18x-15}{3x+x^3}=\frac{(3x-5)(2x^2+6)}{x(x^2+3)}=\frac{3x-5}{x}\).

Ответ: 1) \(\frac{3x-2}{x-5}\); 2) \(\frac1{x+1}\); 3) \(-\frac{3x}{3x-5}\); 4) \(-\frac{x+5}{x-2}\); 5) \(-\frac{2x}{x+3}\); 6) \(\frac1{2x+1}\); 7) \(-\frac{4x^2+6x+9}{x+4}\); 8) \(-\frac{x+6}{x+8}\); 9) \(\frac{x-4}{2x-7}\); 10) \(\frac{3x-5}{x}\).