Simplify 1/(r+7)*(r^2+r-42)/(r+10)

$\frac{1}{r + 7} \cdot \frac{r^{2} + r - 42}{r + 10}$

Step 1

Factor $r^{2} + r - 42$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 42$ and whose sum is $1$ .

$- 6, 7$

Write the factored form using these integers.

$\frac{1}{r + 7} \cdot \frac{(r - 6) (r + 7)}{r + 10}$

Step 2

Cancel the common factor of $r + 7$ .

Factor $r + 7$ out of $(r - 6) (r + 7)$ .

$\frac{1}{r + 7} \cdot \frac{(r + 7) (r - 6)}{r + 10}$

Cancel the common factor.

$\frac{1}{r + 7} \cdot \frac{(r + 7) (r - 6)}{r + 10}$

Rewrite the expression.

$\frac{r - 6}{r + 10}$

Simplify 1/(r+7)*(r^2+r-42)/(r+10)

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