Simplify ((x+11)/(x+2)+11)/((x+11)/(x+2)+2)

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

Step 1

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

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

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

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.

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

Apply the distributive property.

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

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

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

Multiply $2$ by $11$ .

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

Add $x$ and $11 x$ .

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

Add $11$ and $22$ .

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

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

Factor $3$ out of $12 x$ .

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

Factor $3$ out of $33$ .

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

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.

Apply the distributive property.

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

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

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

Multiply $2$ by $2$ .

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

Add $x$ and $2 x$ .

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

Add $11$ and $4$ .

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

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $15$ .

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

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

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

Step 6

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((x+11)/(x+2)+11)/((x+11)/(x+2)+2)

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