Pre-Algebra Examples

$\frac{2 x^{2} + x}{2 x - 2} + \frac{x - 4}{2 x - 2}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{2 x^{2} + x + x - 4}{2 x - 2}$

Step 1.2

Add $x$ and $x$ .

$\frac{2 x^{2} + 2 x - 4}{2 x - 2}$

Step 1.3

Cancel the common factor of $2 x^{2} + 2 x - 4$ and $2 x - 2$ .

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Step 1.3.1

Factor $2$ out of $2 x^{2}$ .

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

Step 1.3.2

Factor $2$ out of $2 x$ .

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

Step 1.3.3

Factor $2$ out of $2 (x^{2}) + 2 (x)$ .

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

Step 1.3.4

Factor $2$ out of $- 4$ .

$\frac{2 (x^{2} + x) + 2 (- 2)}{2 x - 2}$

Step 1.3.5

Factor $2$ out of $2 (x^{2} + x) + 2 (- 2)$ .

$\frac{2 (x^{2} + x - 2)}{2 x - 2}$

Step 1.3.6

Cancel the common factors.

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Step 1.3.6.1

Factor $2$ out of $2 x$ .

$\frac{2 (x^{2} + x - 2)}{2 (x) - 2}$

Step 1.3.6.2

Factor $2$ out of $- 2$ .

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

Step 1.3.6.3

Factor $2$ out of $2 (x) + 2 (- 1)$ .

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

Step 1.3.6.4

Cancel the common factor.

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

Step 1.3.6.5

Rewrite the expression.

$\frac{x^{2} + x - 2}{x - 1}$

Step 2

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

$- 1, 2$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 1) (x + 2)}{x - 1}$

Step 3

Cancel the common factor of $x - 1$ .

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Step 3.1

Cancel the common factor.

$\frac{(x - 1) (x + 2)}{x - 1}$

Step 3.2

Divide $x + 2$ by $1$ .

$x + 2$