Pre-Algebra Examples

$\frac{x^{2}}{x - 7} + \frac{3 x - 70}{x - 7}$

Step 1

Combine the numerators over the common denominator.

$\frac{x^{2} + 3 x - 70}{x - 7}$

Step 2

Factor $x^{2} + 3 x - 70$ 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 $- 70$ and whose sum is $3$ .

$- 7, 10$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 7) (x + 10)}{x - 7}$

Step 3

Cancel the common factor of $x - 7$ .

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Step 3.1

Cancel the common factor.

$\frac{(x - 7) (x + 10)}{x - 7}$

Step 3.2

Divide $x + 10$ by $1$ .

$x + 10$