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ki77a [65]
3 years ago
11

Multiply

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

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)}

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