Question

Напишите подробное решение.

Answer 1

$\frac{x^3+8}{6x^2+11x-2}=\frac{(x+2)(x^2-2x+4)}{6(x+2)(x-\frac{1}{6})}=\frac{x^2-2x+4}{6x-1}\\\\\\\frac{x^2+2x-15}{4x-x^2-3}=\frac{(x-3)(x+5)}{-(x-3)(x-1)}=-\frac{x+5}{x-1}=\frac{x+5}{1-x}$

Answer 2

1)

(х³ + 8) / (6х² + 11х - 2) =

= (х + 2)(х² - 2х + 4) / (6х² + 12х - х - 2) =

= (х + 2)(х² - 2х + 4) / ((6х² + 12х) - (х + 2)) =  

= (х + 2)(х² - 2х + 4) / (6х*(х + 2) - (х + 2)) =  

= (х + 2)(х² - 2х + 4) / (х + 2)(6х - 1) =  

= (х² - 2х + 4) / (6х - 1)

2)

(х² + 2х - 15) / (4х - х² - 3) = (х + 5)(х - 3) / (-(х - 1)(х - 3)) =

= (х + 5) / (-(х - 1) = (х + 5) / (1 - х)