Algebra Examples

$\frac{\frac{x + 11}{x + 2} + 11}{\frac{x + 11}{x + 2} + 2}$

Step 1

Multiply the numerator and denominator of the fraction by $x + 2$ .

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Step 1.1

Multiply $\frac{\frac{x + 11}{x + 2} + 11}{\frac{x + 11}{x + 2} + 2}$ by $\frac{x + 2}{x + 2}$ .

$\frac{x + 2}{x + 2} \cdot \frac{\frac{x + 11}{x + 2} + 11}{\frac{x + 11}{x + 2} + 2}$

Step 1.2

Combine.

$\frac{(x + 2) (\frac{x + 11}{x + 2} + 11)}{(x + 2) (\frac{x + 11}{x + 2} + 2)}$

Step 2

Apply the distributive property.

$\frac{(x + 2) \frac{x + 11}{x + 2} + (x + 2) \cdot 11}{(x + 2) \frac{x + 11}{x + 2} + (x + 2) \cdot 2}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x + 2$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(x + 2) \frac{x + 11}{x + 2} + (x + 2) \cdot 11}{(x + 2) \frac{x + 11}{x + 2} + (x + 2) \cdot 2}$

Step 3.1.2

Rewrite the expression.

$\frac{x + 11 + (x + 2) \cdot 11}{(x + 2) \frac{x + 11}{x + 2} + (x + 2) \cdot 2}$

Step 3.2

Cancel the common factor of $x + 2$ .

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Step 3.2.1

Cancel the common factor.

$\frac{x + 11 + (x + 2) \cdot 11}{(x + 2) \frac{x + 11}{x + 2} + (x + 2) \cdot 2}$

Step 3.2.2

Rewrite the expression.

$\frac{x + 11 + (x + 2) \cdot 11}{x + 11 + (x + 2) \cdot 2}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{x + 11 + x \cdot 11 + 2 \cdot 11}{x + 11 + (x + 2) \cdot 2}$

Step 4.2

Move $11$ to the left of $x$ .

$\frac{x + 11 + 11 \cdot x + 2 \cdot 11}{x + 11 + (x + 2) \cdot 2}$

Step 4.3

Multiply $2$ by $11$ .

$\frac{x + 11 + 11 \cdot x + 22}{x + 11 + (x + 2) \cdot 2}$

Step 4.4

Add $x$ and $11 x$ .

$\frac{12 x + 11 + 22}{x + 11 + (x + 2) \cdot 2}$

Step 4.5

Add $11$ and $22$ .

$\frac{12 x + 33}{x + 11 + (x + 2) \cdot 2}$

Step 4.6

Factor $3$ out of $12 x + 33$ .

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Step 4.6.1

Factor $3$ out of $12 x$ .

$\frac{3 (4 x) + 33}{x + 11 + (x + 2) \cdot 2}$

Step 4.6.2

Factor $3$ out of $33$ .

$\frac{3 (4 x) + 3 (11)}{x + 11 + (x + 2) \cdot 2}$

Step 4.6.3

Factor $3$ out of $3 (4 x) + 3 (11)$ .

$\frac{3 (4 x + 11)}{x + 11 + (x + 2) \cdot 2}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the distributive property.

$\frac{3 (4 x + 11)}{x + 11 + x \cdot 2 + 2 \cdot 2}$

Step 5.2

Move $2$ to the left of $x$ .

$\frac{3 (4 x + 11)}{x + 11 + 2 \cdot x + 2 \cdot 2}$

Step 5.3

Multiply $2$ by $2$ .

$\frac{3 (4 x + 11)}{x + 11 + 2 \cdot x + 4}$

Step 5.4

Add $x$ and $2 x$ .

$\frac{3 (4 x + 11)}{3 x + 11 + 4}$

Step 5.5

Add $11$ and $4$ .

$\frac{3 (4 x + 11)}{3 x + 15}$

Step 5.6

Factor $3$ out of $3 x + 15$ .

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Step 5.6.1

Factor $3$ out of $3 x$ .

$\frac{3 (4 x + 11)}{3 (x) + 15}$

Step 5.6.2

Factor $3$ out of $15$ .

$\frac{3 (4 x + 11)}{3 x + 3 \cdot 5}$

Step 5.6.3

Factor $3$ out of $3 x + 3 \cdot 5$ .

$\frac{3 (4 x + 11)}{3 (x + 5)}$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Cancel the common factor.

$\frac{3 (4 x + 11)}{3 (x + 5)}$

Step 6.2

Rewrite the expression.

$\frac{4 x + 11}{x + 5}$