How do you multiply $\frac{x - 7}{x^{2} + 9 x + 20} \cdot \frac{x + 4}{x^{2} - 49}$ $(x-7)/(x^2+9x+20)*(x+4)/(x^2-49)$ ?

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How do you multiply $\frac{x - 7}{x^{2} + 9 x + 20} \cdot \frac{x + 4}{x^{2} - 49}$ $(x-7)/(x^2+9x+20)*(x+4)/(x^2-49)$ ?

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Answer 1 · 2018-03-12T03:50:14

$\frac{1}{(x + 7) (x + 5)}$ $1/((x+7)(x+5))$

Explanation:

Factorise the denominators first.
$x^{2} + 9 x + 20$ $x^2 + 9x + 20$

The factors that multiply to $c$ $c$ $(20)$ $(20)$ and add to $b$ $b$ $(9)$ $(9)$ are $5$ $5$ and $4$ $4$ .
Therefore $x^{2} + 9 x + 20 = (x + 5) (x + 4)$ $x^2 + 9x + 20 = (x+5)(x+4)$ .

$x^{2} - 49$ $x^2 - 49$ is a difference of two squares.
The formula for a difference of two squares is as follows:
$a^{2} - b^{2} = (a + b) (a - b)$ $a^2 - b^2 = (a+b)(a-b)$

Therefore $x^{2} - 49 = (x + 7) (x - 7)$ $x^2 - 49 = (x+7)(x-7)$ .
Our new expression is $\frac{x - 7}{(x + 4) (x + 5)} \cdot \frac{x + 4}{(x + 7) (x - 7)}$ $(x-7)/((x+4)(x+5)) * (x+4)/((x+7)(x-7)$ .
We can cancel similar brackets.

Our final expression is $\frac{1}{(x + 7) (x + 5)}$ $1/((x+7)(x+5))$ .

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How do you multiply $\frac{x - 7}{x^{2} + 9 x + 20} \cdot \frac{x + 4}{x^{2} - 49}$ $(x-7)/(x^2+9x+20)*(x+4)/(x^2-49)$ ?

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Explanation:

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How do you multiply $\frac{x - 7}{x^{2} + 9 x + 20} \cdot \frac{x + 4}{x^{2} - 49}$ $(x-7)/(x^2+9x+20)*(x+4)/(x^2-49)$ ?