Simplify ((x/2)-3)/(9(x/2)-5)

$\frac{(\frac{x}{2}) - 3}{9 (\frac{x}{2}) - 5}$

Step 1

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

Multiply $\frac{\frac{x}{2} - 3}{9 \frac{x}{2} - 5}$ by $\frac{2}{2}$ .

$\frac{2}{2} \cdot \frac{\frac{x}{2} - 3}{9 \frac{x}{2} - 5}$

Combine.

$\frac{2 (\frac{x}{2} - 3)}{2 (9 \frac{x}{2} - 5)}$

Step 2

Apply the distributive property.

$\frac{2 \frac{x}{2} + 2 \cdot - 3}{2 (9 \frac{x}{2}) + 2 \cdot - 5}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \frac{x}{2} + 2 \cdot - 3}{2 (9 \frac{x}{2}) + 2 \cdot - 5}$

Rewrite the expression.

$\frac{x + 2 \cdot - 3}{2 (9 \frac{x}{2}) + 2 \cdot - 5}$

Multiply $2$ by $- 3$ .

$\frac{x - 6}{2 \cdot 9 \frac{x}{2} + 2 \cdot - 5}$

Step 4

Simplify the denominator.

Factor $2$ out of $2 \cdot 9 \frac{x}{2} + 2 \cdot - 5$ .

Factor $2$ out of $2 \cdot 9 \frac{x}{2}$ .

$\frac{x - 6}{2 (9 \frac{x}{2}) + 2 \cdot - 5}$

Factor $2$ out of $2 \cdot - 5$ .

$\frac{x - 6}{2 (9 \frac{x}{2}) + 2 (- 5)}$

Factor $2$ out of $2 (9 \frac{x}{2}) + 2 (- 5)$ .

$\frac{x - 6}{2 (9 \frac{x}{2} - 5)}$

Combine $9$ and $\frac{x}{2}$ .

$\frac{x - 6}{2 (\frac{9 x}{2} - 5)}$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - 6}{2 (\frac{9 x}{2} - 5 \cdot \frac{2}{2})}$

Combine $- 5$ and $\frac{2}{2}$ .

$\frac{x - 6}{2 (\frac{9 x}{2} + \frac{- 5 \cdot 2}{2})}$

Combine the numerators over the common denominator.

$\frac{x - 6}{2 \frac{9 x - 5 \cdot 2}{2}}$

Multiply $- 5$ by $2$ .

$\frac{x - 6}{2 \frac{9 x - 10}{2}}$

Step 5

Combine $2$ and $\frac{9 x - 10}{2}$ .

$\frac{x - 6}{\frac{2 (9 x - 10)}{2}}$

Step 6

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{2 (9 x - 10)}{2}$ by cancelling the common factors.

Cancel the common factor.

$\frac{x - 6}{\frac{2 (9 x - 10)}{2}}$

Rewrite the expression.

$\frac{x - 6}{\frac{9 x - 10}{1}}$

Divide $9 x - 10$ by $1$ .

$\frac{x - 6}{9 x - 10}$

Simplify ((x/2)-3)/(9(x/2)-5)

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