Algebra Examples

$\frac{x^{2}}{x^{2} - 49} - \frac{9 x - 14}{x^{2} - 49}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

$\frac{x^{2} - (9 x - 14)}{x^{2} - 49}$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$\frac{x^{2} - (9 x) - - 14}{x^{2} - 49}$

Step 1.2.2

Multiply $9$ by $- 1$ .

$\frac{x^{2} - 9 x - - 14}{x^{2} - 49}$

Step 1.2.3

Multiply $- 1$ by $- 14$ .

$\frac{x^{2} - 9 x + 14}{x^{2} - 49}$

Step 2

Factor $x^{2} - 9 x + 14$ 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 $- 9$ .

$- 7, - 2$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 7) (x - 2)}{x^{2} - 49}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $49$ as $7^{2}$ .

$\frac{(x - 7) (x - 2)}{x^{2} - 7^{2}}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 7$ .

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

Step 4

Cancel the common factor of $x - 7$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{x - 2}{x + 7}$