Pre-Algebra Examples

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

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

Step 1

Combine the numerators over the common denominator.

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

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

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

4 x = 2 \cdot x \cdot 2

$4 x = 2 \cdot x \cdot 2$

Step 2.3

Rewrite the polynomial.

\frac{x^{2} + 2 \cdot x \cdot 2 + 2^{2}}{x + 2}

$\frac{x^{2} + 2 \cdot x \cdot 2 + 2^{2}}{x + 2}$

Step 2.4

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

a = x

$a = x$ and

b = 2

$b = 2$ .

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

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

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

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

Step 3

Cancel the common factor of

{(x + 2)}^{2}

${(x + 2)}^{2}$ and

x + 2

$x + 2$ .

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Step 3.1

Factor

x + 2

$x + 2$ out of

{(x + 2)}^{2}

${(x + 2)}^{2}$ .

\frac{(x + 2) (x + 2)}{x + 2}

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by

1

$1$ .

\frac{(x + 2) (x + 2)}{(x + 2) \cdot 1}

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide

$x + 2$ by

$1$ .

$x + 2$