Simplify (x^2-x-20)/(x^2-13x+40)

$\frac{x^{2} - x - 20}{x^{2} - 13 x + 40}$

Step 1

Factor $x^{2} - x - 20$ 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 $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Write the factored form using these integers.

$\frac{(x - 5) (x + 4)}{x^{2} - 13 x + 40}$

Step 2

Factor $x^{2} - 13 x + 40$ 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 $40$ and whose sum is $- 13$ .

$- 8, - 5$

Write the factored form using these integers.

$\frac{(x - 5) (x + 4)}{(x - 8) (x - 5)}$

Step 3

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{(x - 5) (x + 4)}{(x - 8) (x - 5)}$

Rewrite the expression.

$\frac{x + 4}{x - 8}$

Simplify (x^2-x-20)/(x^2-13x+40)

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