Question

Multiply

Answer 1

Answer:

The product of given two fractions is

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

Therefore $\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}=\frac{4(x+2)}{(x-1)(x+3)}$

Step-by-step explanation:

Given expression is  

$\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}$

To find the product of two given fractions as below :

$\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}=\frac{2(5)}{x(x-1)}\times \frac{2x(x+2)}{5(x+3)}$

$=\frac{10}{x(x-1)}\times \frac{2x(x+2)}{5(x+3)}$

$=\frac{20x(x+2)}{5x(x-1)(x+3)}$

$=\frac{20x^2+40x}{(5x^2-5x)(x+3)}$ (multiply each term in the factor to each term in the another factor )

$=\frac{20x^2+40x}{5x^3+15x^2-5x^2-15x}$  ( adding the like terms )

$=\frac{20x^2+40x}{5x^3+10x^2-15x}$

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

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

Therefore $\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}=\frac{4(x+2)}{(x-1)(x+3)}$

Therefore the product of given two fractions is $\frac{4(x+2)}{(x-1)(x+3)}$