Answer:
The product of given two fractions is
[tex]\frac{4(x+2)}{(x-1)(x+3)}[/tex]
Therefore [tex]\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}=\frac{4(x+2)}{(x-1)(x+3)}[/tex]
Step-by-step explanation:
Given expression is
[tex]\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}[/tex]
To find the product of two given fractions as below :
[tex]\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)}[/tex]
[tex]=\frac{10}{x(x-1)}\times \frac{2x(x+2)}{5(x+3)}[/tex]
[tex]=\frac{20x(x+2)}{5x(x-1)(x+3)}[/tex]
[tex]=\frac{20x^2+40x}{(5x^2-5x)(x+3)}[/tex] (multiply each term in the factor to each term in the another factor )
[tex]=\frac{20x^2+40x}{5x^3+15x^2-5x^2-15x}[/tex] ( adding the like terms )
[tex]=\frac{20x^2+40x}{5x^3+10x^2-15x}[/tex]
[tex]=\frac{5x(4x+8)}{5x(x^2+2x-3)}[/tex]
[tex]=\frac{4(x+2)}{(x-1)(x+3)}[/tex]
Therefore [tex]\frac{2(2+3)}{x(x-1)}\times \frac{4x(x+2)}{10(x+3)}=\frac{4(x+2)}{(x-1)(x+3)}[/tex]
Therefore the product of given two fractions is [tex]\frac{4(x+2)}{(x-1)(x+3)}[/tex]
