Pre-Algebra Examples

$\frac{y^{2} + 14}{x^{2} + 4 x - 5}$

Step 1

Factor $x^{2} + 4 x - 5$ using the AC method.

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Step 1.1

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 $- 5$ and whose sum is $4$ .

$- 1, 5$

Step 1.2

Write the factored form using these integers.

$\frac{y^{2} + 14}{(x - 1) (x + 5)}$

Step 2

Split the fraction $\frac{y^{2} + 14}{(x - 1) (x + 5)}$ into two fractions.

$\frac{y^{2}}{(x - 1) (x + 5)} + \frac{14}{(x - 1) (x + 5)}$