Algebra Examples

$\frac{5 (\frac{x}{2}) - 1}{9 (\frac{x}{2}) - 4}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\frac{5 x}{2} - 1}{9 \frac{x}{2} - 4}$

Step 1.2

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

$\frac{\frac{5 x}{2} - 1 \cdot \frac{2}{2}}{9 \frac{x}{2} - 4}$

Step 1.3

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

$\frac{\frac{5 x}{2} + \frac{- 1 \cdot 2}{2}}{9 \frac{x}{2} - 4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{\frac{5 x - 1 \cdot 2}{2}}{9 \frac{x}{2} - 4}$

Step 1.5

Multiply $- 1$ by $2$ .

$\frac{\frac{5 x - 2}{2}}{9 \frac{x}{2} - 4}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\frac{5 x - 2}{2}}{\frac{9 x}{2} - 4}$

Step 2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{5 x - 2}{2}}{\frac{9 x}{2} - 4 \cdot \frac{2}{2}}$

Step 2.3

Combine $- 4$ and $\frac{2}{2}$ .

$\frac{\frac{5 x - 2}{2}}{\frac{9 x}{2} + \frac{- 4 \cdot 2}{2}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{5 x - 2}{2}}{\frac{9 x - 4 \cdot 2}{2}}$

Step 2.5

Multiply $- 4$ by $2$ .

$\frac{\frac{5 x - 2}{2}}{\frac{9 x - 8}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 x - 2}{2} \cdot \frac{2}{9 x - 8}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$\frac{5 x - 2}{2} \cdot \frac{2}{9 x - 8}$

Step 4.2

Rewrite the expression.

$(5 x - 2) \frac{1}{9 x - 8}$

Step 5

Multiply $5 x - 2$ by $\frac{1}{9 x - 8}$ .

$\frac{5 x - 2}{9 x - 8}$