Simplify (x+8)/(x+2)+1/((x+8)/(x+2))

$\frac{x + 8}{x + 2} + \frac{1}{\frac{x + 8}{x + 2}}$

Step 1

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$\frac{x + 8}{x + 2} + 1 \frac{x + 2}{x + 8}$

Multiply $\frac{x + 2}{x + 8}$ by $1$ .

$\frac{x + 8}{x + 2} + \frac{x + 2}{x + 8}$

Step 2

To write $\frac{x + 8}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x + 8}{x + 8}$ .

$\frac{x + 8}{x + 2} \cdot \frac{x + 8}{x + 8} + \frac{x + 2}{x + 8}$

Step 3

To write $\frac{x + 2}{x + 8}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$\frac{x + 8}{x + 2} \cdot \frac{x + 8}{x + 8} + \frac{x + 2}{x + 8} \cdot \frac{x + 2}{x + 2}$

Step 4

Write each expression with a common denominator of $(x + 2) (x + 8)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 8}{x + 2}$ by $\frac{x + 8}{x + 8}$ .

$\frac{(x + 8) (x + 8)}{(x + 2) (x + 8)} + \frac{x + 2}{x + 8} \cdot \frac{x + 2}{x + 2}$

Multiply $\frac{x + 2}{x + 8}$ by $\frac{x + 2}{x + 2}$ .

$\frac{(x + 8) (x + 8)}{(x + 2) (x + 8)} + \frac{(x + 2) (x + 2)}{(x + 8) (x + 2)}$

Reorder the factors of $(x + 8) (x + 2)$ .

$\frac{(x + 8) (x + 8)}{(x + 2) (x + 8)} + \frac{(x + 2) (x + 2)}{(x + 2) (x + 8)}$

Step 5

Combine the numerators over the common denominator.

$\frac{(x + 8) (x + 8) + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Step 6

Simplify the numerator.

Expand $(x + 8) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$\frac{x (x + 8) + 8 (x + 8) + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Apply the distributive property.

$\frac{x \cdot x + x \cdot 8 + 8 (x + 8) + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Apply the distributive property.

$\frac{x \cdot x + x \cdot 8 + 8 x + 8 \cdot 8 + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot 8 + 8 x + 8 \cdot 8 + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Move $8$ to the left of $x$ .

$\frac{x^{2} + 8 \cdot x + 8 x + 8 \cdot 8 + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Multiply $8$ by $8$ .

$\frac{x^{2} + 8 x + 8 x + 64 + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Add $8 x$ and $8 x$ .

$\frac{x^{2} + 16 x + 64 + (x + 2) (x + 2)}{(x + 2) (x + 8)}$

Expand $(x + 2) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$\frac{x^{2} + 16 x + 64 + x (x + 2) + 2 (x + 2)}{(x + 2) (x + 8)}$

Apply the distributive property.

$\frac{x^{2} + 16 x + 64 + x \cdot x + x \cdot 2 + 2 (x + 2)}{(x + 2) (x + 8)}$

Apply the distributive property.

$\frac{x^{2} + 16 x + 64 + x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2}{(x + 2) (x + 8)}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{x^{2} + 16 x + 64 + x^{2} + x \cdot 2 + 2 x + 2 \cdot 2}{(x + 2) (x + 8)}$

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

$\frac{x^{2} + 16 x + 64 + x^{2} + 2 \cdot x + 2 x + 2 \cdot 2}{(x + 2) (x + 8)}$

Multiply $2$ by $2$ .

$\frac{x^{2} + 16 x + 64 + x^{2} + 2 x + 2 x + 4}{(x + 2) (x + 8)}$

Add $2 x$ and $2 x$ .

$\frac{x^{2} + 16 x + 64 + x^{2} + 4 x + 4}{(x + 2) (x + 8)}$

Add $x^{2}$ and $x^{2}$ .

$\frac{2 x^{2} + 16 x + 64 + 4 x + 4}{(x + 2) (x + 8)}$

Add $16 x$ and $4 x$ .

$\frac{2 x^{2} + 20 x + 64 + 4}{(x + 2) (x + 8)}$

Add $64$ and $4$ .

$\frac{2 x^{2} + 20 x + 68}{(x + 2) (x + 8)}$

Factor $2$ out of $2 x^{2} + 20 x + 68$ .

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

$\frac{2 (x^{2}) + 20 x + 68}{(x + 2) (x + 8)}$

Factor $2$ out of $20 x$ .

$\frac{2 (x^{2}) + 2 (10 x) + 68}{(x + 2) (x + 8)}$

Factor $2$ out of $68$ .

$\frac{2 x^{2} + 2 (10 x) + 2 \cdot 34}{(x + 2) (x + 8)}$

Factor $2$ out of $2 x^{2} + 2 (10 x)$ .

$\frac{2 (x^{2} + 10 x) + 2 \cdot 34}{(x + 2) (x + 8)}$

Factor $2$ out of $2 (x^{2} + 10 x) + 2 \cdot 34$ .

$\frac{2 (x^{2} + 10 x + 34)}{(x + 2) (x + 8)}$

Simplify (x+8)/(x+2)+1/((x+8)/(x+2))

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