[tex]\frac{x-4}{x^3-x} : (\frac{x-1}{2x^2+3x+1}-\frac{1}{x^2-1})[/tex] Упростить выражение.. Created by Metallist. algebra-ru

решение в прикреплённом файле

tex] Упростить выражение...

Svet1ana

Verified answer

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

1) $\frac{x-1}{2x^2+3x+1}-\frac{1}{x^2-1}=\frac{x-1}{(2x+1)(x+1)}-\frac{1}{(x+1)(x-1)}= \frac{(x-1)(x-1)-(2x+1)}{(2x+1)(x+1)(x-1)}=\frac{(x^{2}-x-x+1)-(2x+1)}{(2x+1)(x+1)(x-1)}=$ = $\frac{x^{2}-2x+1-2x-1}{(2x+1)(x+1)(x-1)}=\frac{x^{2}-(2x+2x)+(1-1)}{(2x+1)(x+1)(x-1)}=\frac{x^{2}-4x}{(2x+1)(x+1)(x-1)}$

2) $\frac{x-4}{x^3-x} : \frac{x^{2}-4x}{(2x+1)(x+1)(x-1)}=\frac{x-4}{x(x^{2}-1)} : \frac{x^{2}-4x}{(2x+1)(x+1)(x-1)}=\frac{x-4}{x(x-1)(x+1)} : \frac{x(x-4)}{(2x+1)(x+1)(x-1)}=$ = $\frac{x-4}{x(x-1)(x+1)}\cdot\frac{(2x+1)(x+1)(x-1)}{x(x-4)}=\frac{2x+1}{x^{2}}$

1 votes Thanks 0

Answers & Comments

Verified answer

Verified answer

drobnaya cherta x2 stepen 3x umnozhenie

tex5b4d1f57bc607ef5b0b9dc585d4bce1c 63957

ch93c0aef4ba62dfadcd84b2ea2bdcff32 62713

tex reshite neravenstvo0cc1ff4fa6259cd2e6485d74e3ebee47 21830

tex]...

napisat obrashenie ko vsem vzroslym na zemle o prekrashenii vojn podrobno

tex]...

рекомендуемые вопросы

Helpful Links

Helpful Social