Basic Math Examples

$\frac{a^{2}}{a - 4} + \frac{2 a + 8}{4 - a}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Factor $2$ out of $2 a + 8$ .

Tap for more steps...

Step 1.1.1

Factor $2$ out of $2 a$ .

$\frac{a^{2}}{a - 4} + \frac{2 (a) + 8}{4 - a}$

Step 1.1.2

Factor $2$ out of $8$ .

$\frac{a^{2}}{a - 4} + \frac{2 a + 2 \cdot 4}{4 - a}$

Step 1.1.3

Factor $2$ out of $2 a + 2 \cdot 4$ .

$\frac{a^{2}}{a - 4} + \frac{2 (a + 4)}{4 - a}$

Step 1.2

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{a^{2}}{a - 4} + \frac{2 (a + 4)}{- 1 (- 4) - a}$

Step 1.3

Factor $- 1$ out of $- a$ .

$\frac{a^{2}}{a - 4} + \frac{2 (a + 4)}{- 1 (- 4) - (a)}$

Step 1.4

Factor $- 1$ out of $- 1 (- 4) - (a)$ .

$\frac{a^{2}}{a - 4} + \frac{2 (a + 4)}{- 1 (- 4 + a)}$

Step 1.5

Simplify the expression.

Tap for more steps...

Step 1.5.1

Move a negative from the denominator of $\frac{2 (a + 4)}{- 1 (- 4 + a)}$ to the numerator.

$\frac{a^{2}}{a - 4} + \frac{- (2 (a + 4))}{- 4 + a}$

Step 1.5.2

Reorder terms.

$\frac{a^{2}}{a - 4} + \frac{- (2 (a + 4))}{a - 4}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{a^{2} - (2 (a + 4))}{a - 4}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Multiply $- 1$ by $2$ .

$\frac{a^{2} - 2 (a + 4)}{a - 4}$

Step 2.2

Apply the distributive property.

$\frac{a^{2} - 2 a - 2 \cdot 4}{a - 4}$

Step 2.3

Multiply $- 2$ by $4$ .

$\frac{a^{2} - 2 a - 8}{a - 4}$

Step 2.4

Factor $a^{2} - 2 a - 8$ using the AC method.

Tap for more steps...

Step 2.4.1

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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Step 2.4.2

Write the factored form using these integers.

$\frac{(a - 4) (a + 2)}{a - 4}$

Step 3

Cancel the common factor of $a - 4$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{(a - 4) (a + 2)}{a - 4}$

Step 3.2

Divide $a + 2$ by $1$ .

$a + 2$