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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

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

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

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Multiply $- 5$ by $2$ .

$\frac{2 \frac{9 x - 10}{2}}{x + 2 \cdot - 3}$

Step 5

Combine fractions.

Multiply $2$ by $- 3$ .

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

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

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

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.

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

Rewrite the expression.

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

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

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

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

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