Simplify (7(x/2)-3)/(5(x/2)-1)

$\frac{7 (\frac{x}{2}) - 3}{5 (\frac{x}{2}) - 1}$

Step 1

Simplify the numerator.

Combine $7$ and $\frac{x}{2}$ .

$\frac{\frac{7 x}{2} - 3}{5 \frac{x}{2} - 1}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{7 x}{2} - 3 \cdot \frac{2}{2}}{5 \frac{x}{2} - 1}$

Combine $- 3$ and $\frac{2}{2}$ .

$\frac{\frac{7 x}{2} + \frac{- 3 \cdot 2}{2}}{5 \frac{x}{2} - 1}$

Combine the numerators over the common denominator.

$\frac{\frac{7 x - 3 \cdot 2}{2}}{5 \frac{x}{2} - 1}$

Multiply $- 3$ by $2$ .

$\frac{\frac{7 x - 6}{2}}{5 \frac{x}{2} - 1}$

Step 2

Simplify the denominator.

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

$\frac{\frac{7 x - 6}{2}}{\frac{5 x}{2} - 1}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{7 x - 6}{2}}{\frac{5 x}{2} - 1 \cdot \frac{2}{2}}$

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{\frac{7 x - 6}{2}}{\frac{5 x}{2} + \frac{- 1 \cdot 2}{2}}$

Combine the numerators over the common denominator.

$\frac{\frac{7 x - 6}{2}}{\frac{5 x - 1 \cdot 2}{2}}$

Multiply $- 1$ by $2$ .

$\frac{\frac{7 x - 6}{2}}{\frac{5 x - 2}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 x - 6}{2} \cdot \frac{2}{5 x - 2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 x - 6}{2} \cdot \frac{2}{5 x - 2}$

Rewrite the expression.

$(7 x - 6) \frac{1}{5 x - 2}$

Step 5

Multiply $7 x - 6$ by $\frac{1}{5 x - 2}$ .

$\frac{7 x - 6}{5 x - 2}$