Pre-Algebra Examples

$\frac{5 x - 5}{x^{2} - 2 x - 15} + \frac{- 4 x + 8}{x^{2} - 2 x - 15}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{5 x - 5 - 4 x + 8}{x^{2} - 2 x - 15}$

Step 1.2

Subtract $4 x$ from $5 x$ .

$\frac{x - 5 + 8}{x^{2} - 2 x - 15}$

Step 1.3

Add $- 5$ and $8$ .

$\frac{x + 3}{x^{2} - 2 x - 15}$

Step 2

Factor $x^{2} - 2 x - 15$ using the AC method.

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Step 2.1

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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Step 2.2

Write the factored form using these integers.

$\frac{x + 3}{(x - 5) (x + 3)}$

Step 3

Cancel the common factor of $x + 3$ .

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Step 3.1

Cancel the common factor.

$\frac{x + 3}{(x - 5) (x + 3)}$

Step 3.2

Rewrite the expression.

$\frac{1}{x - 5}$