Algebra Examples

$\frac{\frac{4}{x + 1} + \frac{2}{x}}{\frac{2}{x + 1}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{4}{x + 1} + \frac{2}{x}) \frac{x + 1}{2}$

Step 2

To write $\frac{4}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{4}{x + 1} \cdot \frac{x}{x} + \frac{2}{x}) \frac{x + 1}{2}$

Step 3

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

$(\frac{4}{x + 1} \cdot \frac{x}{x} + \frac{2}{x} \cdot \frac{x + 1}{x + 1}) \frac{x + 1}{2}$

Step 4

Write each expression with a common denominator of $(x + 1) x$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{4}{x + 1}$ by $\frac{x}{x}$ .

$(\frac{4 x}{(x + 1) x} + \frac{2}{x} \cdot \frac{x + 1}{x + 1}) \frac{x + 1}{2}$

Step 4.2

Multiply $\frac{2}{x}$ by $\frac{x + 1}{x + 1}$ .

$(\frac{4 x}{(x + 1) x} + \frac{2 (x + 1)}{x (x + 1)}) \frac{x + 1}{2}$

Step 4.3

Reorder the factors of $(x + 1) x$ .

$(\frac{4 x}{x (x + 1)} + \frac{2 (x + 1)}{x (x + 1)}) \frac{x + 1}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 x + 2 (x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Factor $2$ out of $4 x + 2 (x + 1)$ .

Tap for more steps...

Step 6.1.1

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) + 2 (x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Step 6.1.2

Factor $2$ out of $2 (2 x) + 2 (x + 1)$ .

$\frac{2 (2 x + x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Step 6.2

Add $2 x$ and $x$ .

$\frac{2 (3 x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Step 7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 7.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1.1

Cancel the common factor.

$\frac{2 (3 x + 1)}{x (x + 1)} \cdot \frac{x + 1}{2}$

Step 7.1.2

Rewrite the expression.

$\frac{3 x + 1}{x (x + 1)} (x + 1)$

Step 7.2

Cancel the common factor of $x + 1$ .

Tap for more steps...

Step 7.2.1

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

$\frac{3 x + 1}{(x + 1) x} (x + 1)$

Step 7.2.2

Cancel the common factor.

$\frac{3 x + 1}{(x + 1) x} (x + 1)$

Step 7.2.3

Rewrite the expression.

$\frac{3 x + 1}{x}$