Algebra Examples

$\frac{\frac{5 q}{q + 1}}{1 - \frac{q}{q + 1}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 q}{q + 1} \cdot \frac{1}{1 - \frac{q}{q + 1}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{5 q}{q + 1} \cdot \frac{1}{\frac{q + 1}{q + 1} - \frac{q}{q + 1}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{5 q}{q + 1} \cdot \frac{1}{\frac{q + 1 - q}{q + 1}}$

Step 2.3

Reorder terms.

$\frac{5 q}{q + 1} \cdot \frac{1}{\frac{q - q + 1}{q + 1}}$

Step 2.4

Rewrite $\frac{q - q + 1}{q + 1}$ in a factored form.

Tap for more steps...

Step 2.4.1

Subtract $q$ from $q$ .

$\frac{5 q}{q + 1} \cdot \frac{1}{\frac{0 + 1}{q + 1}}$

Step 2.4.2

Add $0$ and $1$ .

$\frac{5 q}{q + 1} \cdot \frac{1}{\frac{1}{q + 1}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 q}{q + 1} (1 (q + 1))$

Step 4

Cancel the common factor of $q + 1$ .

Tap for more steps...

Step 4.1

Factor $q + 1$ out of $1 (q + 1)$ .

$\frac{5 q}{q + 1} ((q + 1) \cdot 1)$

Step 4.2

Cancel the common factor.

$\frac{5 q}{q + 1} ((q + 1) \cdot 1)$

Step 4.3

Rewrite the expression.

$5 q$