Pre-Algebra Examples

$\frac{x + 2}{x - 1} \div \frac{x + 4}{x^{2} + 4 x - 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Factor $x^{2} + 4 x - 5$ using the AC method.

Tap for more steps...

Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 5$ and whose sum is $4$ .

$- 1, 5$

Step 2.2

Write the factored form using these integers.

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $x - 1$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$(x + 2) \frac{x + 5}{x + 4}$

Step 3.2

Multiply $x + 2$ by $\frac{x + 5}{x + 4}$ .

$\frac{(x + 2) (x + 5)}{x + 4}$