Algebra Examples

$\frac{x - 2}{x^{2} + x - 6} \div \frac{x^{2} + 5 x + 4}{x + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 2}{x^{2} + x - 6} \cdot \frac{x + 4}{x^{2} + 5 x + 4}$

Step 2

Factor $x^{2} + x - 6$ 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 2.2

Write the factored form using these integers.

$\frac{x - 2}{(x - 2) (x + 3)} \cdot \frac{x + 4}{x^{2} + 5 x + 4}$

Step 3

Cancel the common factor of $x - 2$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{x - 2}{(x - 2) (x + 3)} \cdot \frac{x + 4}{x^{2} + 5 x + 4}$

Step 3.2

Rewrite the expression.

$\frac{1}{x + 3} \cdot \frac{x + 4}{x^{2} + 5 x + 4}$

Step 4

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

Tap for more steps...

Step 4.1

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 $4$ and whose sum is $5$ .

$1, 4$

Step 4.2

Write the factored form using these integers.

$\frac{1}{x + 3} \cdot \frac{x + 4}{(x + 1) (x + 4)}$

Step 5

Simplify terms.

Tap for more steps...

Step 5.1

Cancel the common factor of $x + 4$ .

Tap for more steps...

Step 5.1.1

Cancel the common factor.

$\frac{1}{x + 3} \cdot \frac{x + 4}{(x + 1) (x + 4)}$

Step 5.1.2

Rewrite the expression.

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

Step 5.2

Multiply $\frac{1}{x + 3}$ by $\frac{1}{x + 1}$ .

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