Pre-Algebra Examples

$\frac{\frac{x + 2}{x^{2} - 5 x - 14}}{\frac{x^{2} - x - 6}{x^{2} - 10 x + 21}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x + 2}{x^{2} - 5 x - 14} \cdot \frac{x^{2} - 10 x + 21}{x^{2} - x - 6}$

Step 2

Factor $x^{2} - 5 x - 14$ 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 $- 14$ and whose sum is $- 5$ .

$- 7, 2$

Step 2.2

Write the factored form using these integers.

$\frac{x + 2}{(x - 7) (x + 2)} \cdot \frac{x^{2} - 10 x + 21}{x^{2} - x - 6}$

Step 3

Cancel the common factor of $x + 2$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{x + 2}{(x - 7) (x + 2)} \cdot \frac{x^{2} - 10 x + 21}{x^{2} - x - 6}$

Step 3.2

Rewrite the expression.

$\frac{1}{x - 7} \cdot \frac{x^{2} - 10 x + 21}{x^{2} - x - 6}$

Step 4

Factor $x^{2} - 10 x + 21$ 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 $21$ and whose sum is $- 10$ .

$- 7, - 3$

Step 4.2

Write the factored form using these integers.

$\frac{1}{x - 7} \cdot \frac{(x - 7) (x - 3)}{x^{2} - x - 6}$

Step 5

Factor $x^{2} - x - 6$ using the AC method.

Tap for more steps...

Step 5.1

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 $- 1$ .

$- 3, 2$

Step 5.2

Write the factored form using these integers.

$\frac{1}{x - 7} \cdot \frac{(x - 7) (x - 3)}{(x - 3) (x + 2)}$

Step 6

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 6.1

Cancel the common factor of $x - 7$ .

Tap for more steps...

Step 6.1.1

Cancel the common factor.

$\frac{1}{x - 7} \cdot \frac{(x - 7) (x - 3)}{(x - 3) (x + 2)}$

Step 6.1.2

Rewrite the expression.

$\frac{x - 3}{(x - 3) (x + 2)}$

Step 6.2

Cancel the common factor of $x - 3$ .

Tap for more steps...

Step 6.2.1

Cancel the common factor.

$\frac{x - 3}{(x - 3) (x + 2)}$

Step 6.2.2

Rewrite the expression.

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