44. Упростите: 1) $\frac{9c^2-16}{16-24c+9c^2}$; 2) $\frac{16x^2-24xy+9y^2}{9y^2-16x^2}$; 3) $\frac{4x^2-4xy+y^2}{y^2-4x^2}$; 4) $\frac{36c-c^3}{c^3+12c^2+36c}$; 5) $\frac{25b-49b^3}{49b^3-70b^2+25b}$; 6) $\frac{4b^2-12bc+9c^2}{-2ab+3ac}$.

Question

Вопрос: $Фото задания: 44. Упростите: 1) $\frac{9c^2-16}{16-24c+9c^2}$; 2) $\frac{16x^2-24xy+9y^2}{9y^2-16x^2}$; 3)…$ Фото задания

44. Упростите: 1) $\frac{9c^2-16}{16-24c+9c^2}$; 2) $\frac{16x^2-24xy+9y^2}{9y^2-16x^2}$; 3) $\frac{4x^2-4xy+y^2}{y^2-4x^2}$; 4) $\frac{36c-c^3}{c^3+12c^2+36c}$; 5) $\frac{25b-49b^3}{49b^3-70b^2+25b}$; 6) $\frac{4b^2-12bc+9c^2}{-2ab+3ac}$.

Accepted Answer

1) $9c^2-16=(3c-4)(3c+4)$, $16-24c+9c^2=(3c-4)^2$.

$\frac{9c^2-16}{16-24c+9c^2}=\frac{3c+4}{3c-4}$.

2) $16x^2-24xy+9y^2=(4x-3y)^2$, $9y^2-16x^2=-(4x-3y)(4x+3y)$.

$\frac{16x^2-24xy+9y^2}{9y^2-16x^2}=-\frac{4x-3y}{4x+3y}=\frac{3y-4x}{4x+3y}$.

3) $4x^2-4xy+y^2=(2x-y)^2$, $y^2-4x^2=-(2x-y)(2x+y)$.

$\frac{4x^2-4xy+y^2}{y^2-4x^2}=\frac{y-2x}{y+2x}$.

4) $36c-c^3=c(6-c)(6+c)$, $c^3+12c^2+36c=c(c+6)^2$.

$\frac{36c-c^3}{c^3+12c^2+36c}=\frac{6-c}{c+6}$.

5) $25b-49b^3=b(5-7b)(5+7b)$, $49b^3-70b^2+25b=b(7b-5)^2=b(5-7b)^2$.

$\frac{25b-49b^3}{49b^3-70b^2+25b}=\frac{5+7b}{5-7b}$.

6) $4b^2-12bc+9c^2=(2b-3c)^2$, $-2ab+3ac=-a(2b-3c)$.

$\frac{4b^2-12bc+9c^2}{-2ab+3ac}=\frac{3c-2b}{a}$.

Ответ: 1) $\frac{3c+4}{3c-4}$; 2) $\frac{3y-4x}{4x+3y}$; 3) $\frac{y-2x}{y+2x}$; 4) $\frac{6-c}{c+6}$; 5) $\frac{5+7b}{5-7b}$; 6) $\frac{3c-2b}{a}$.

44. Упростите: 1) \(\frac{9c^2-16}{16-24c+9c^2}\); 2) \(\frac{16x^2-24xy+9y^2}{9y^2-16x^2}\); 3) \(\frac{4x^2-4xy+y^2}{y^2-4x^2}\); 4) \(\frac{36c-c^3}{c^3+12c^2+36c}\); 5) \(\frac{25b-49b^3}{49b^3-70b^2+25b}\); 6) \(\frac{4b^2-12bc+9c^2}{-2ab+3ac}\).

Ответ: