Simplify ((x+17)/x+7)/((x+10)/x+7)

$\frac{\frac{x + 17}{x} + 7}{\frac{x + 10}{x} + 7}$

Step 1

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

Multiply $\frac{\frac{x + 17}{x} + 7}{\frac{x + 10}{x} + 7}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{\frac{x + 17}{x} + 7}{\frac{x + 10}{x} + 7}$

Combine.

$\frac{x (\frac{x + 17}{x} + 7)}{x (\frac{x + 10}{x} + 7)}$

Step 2

Apply the distributive property.

$\frac{x \frac{x + 17}{x} + x \cdot 7}{x \frac{x + 10}{x} + x \cdot 7}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x \frac{x + 17}{x} + x \cdot 7}{x \frac{x + 10}{x} + x \cdot 7}$

Rewrite the expression.

$\frac{x + 17 + x \cdot 7}{x \frac{x + 10}{x} + x \cdot 7}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x + 17 + x \cdot 7}{x \frac{x + 10}{x} + x \cdot 7}$

Rewrite the expression.

$\frac{x + 17 + x \cdot 7}{x + 10 + x \cdot 7}$

Step 4

Simplify the numerator.

Move $7$ to the left of $x$ .

$\frac{x + 17 + 7 \cdot x}{x + 10 + x \cdot 7}$

Add $x$ and $7 x$ .

$\frac{8 x + 17}{x + 10 + x \cdot 7}$

Step 5

Simplify the denominator.

Add $x$ and $x \cdot 7$ .

Reorder $x$ and $7$ .

$\frac{8 x + 17}{x + 7 \cdot x + 10}$

Add $x$ and $7 \cdot x$ .

$\frac{8 x + 17}{8 x + 10}$

Factor $2$ out of $8 x + 10$ .

Factor $2$ out of $8 x$ .

$\frac{8 x + 17}{2 (4 x) + 10}$

Factor $2$ out of $10$ .

$\frac{8 x + 17}{2 (4 x) + 2 (5)}$

Factor $2$ out of $2 (4 x) + 2 (5)$ .

$\frac{8 x + 17}{2 (4 x + 5)}$