Algebra Examples

$2 x - 5 - \frac{x - 8}{x + 4}$

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

Write $2 x$ as a fraction with denominator $1$ .

$\frac{2 x}{1} - 5 - \frac{x - 8}{x + 4}$

Step 1.2

Multiply $\frac{2 x}{1}$ by $\frac{x + 4}{x + 4}$ .

$\frac{2 x}{1} \cdot \frac{x + 4}{x + 4} - 5 - \frac{x - 8}{x + 4}$

Step 1.3

Multiply $\frac{2 x}{1}$ by $\frac{x + 4}{x + 4}$ .

$\frac{2 x (x + 4)}{x + 4} - 5 - \frac{x - 8}{x + 4}$

Step 1.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{2 x (x + 4)}{x + 4} + \frac{- 5}{1} - \frac{x - 8}{x + 4}$

Step 1.5

Multiply $\frac{- 5}{1}$ by $\frac{x + 4}{x + 4}$ .

$\frac{2 x (x + 4)}{x + 4} + \frac{- 5}{1} \cdot \frac{x + 4}{x + 4} - \frac{x - 8}{x + 4}$

Step 1.6

Multiply $\frac{- 5}{1}$ by $\frac{x + 4}{x + 4}$ .

$\frac{2 x (x + 4)}{x + 4} + \frac{- 5 (x + 4)}{x + 4} - \frac{x - 8}{x + 4}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{2 x (x + 4) - 5 (x + 4) - (x - 8)}{x + 4}$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

$\frac{2 x \cdot x + 2 x \cdot 4 - 5 (x + 4) - (x - 8)}{x + 4}$

Step 2.2.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 2.2.2.1

Move $x$ .

$\frac{2 (x \cdot x) + 2 x \cdot 4 - 5 (x + 4) - (x - 8)}{x + 4}$

Step 2.2.2.2

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 2 x \cdot 4 - 5 (x + 4) - (x - 8)}{x + 4}$

Step 2.2.3

Multiply $4$ by $2$ .

$\frac{2 x^{2} + 8 x - 5 (x + 4) - (x - 8)}{x + 4}$

Step 2.2.4

Apply the distributive property.

$\frac{2 x^{2} + 8 x - 5 x - 5 \cdot 4 - (x - 8)}{x + 4}$

Step 2.2.5

Multiply $- 5$ by $4$ .

$\frac{2 x^{2} + 8 x - 5 x - 20 - (x - 8)}{x + 4}$

Step 2.2.6

Apply the distributive property.

$\frac{2 x^{2} + 8 x - 5 x - 20 - x - - 8}{x + 4}$

Step 2.2.7

Multiply $- 1$ by $- 8$ .

$\frac{2 x^{2} + 8 x - 5 x - 20 - x + 8}{x + 4}$

Step 2.3

Simplify by adding terms.

Tap for more steps...

Step 2.3.1

Subtract $5 x$ from $8 x$ .

$\frac{2 x^{2} + 3 x - 20 - x + 8}{x + 4}$

Step 2.3.2

Subtract $x$ from $3 x$ .

$\frac{2 x^{2} + 2 x - 20 + 8}{x + 4}$

Step 2.3.3

Add $- 20$ and $8$ .

$\frac{2 x^{2} + 2 x - 12}{x + 4}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Factor $2$ out of $2 x^{2} + 2 x - 12$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (x^{2}) + 2 x - 12}{x + 4}$

Step 3.1.2

Factor $2$ out of $2 x$ .

$\frac{2 (x^{2}) + 2 (x) - 12}{x + 4}$

Step 3.1.3

Factor $2$ out of $- 12$ .

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

Step 3.1.4

Factor $2$ out of $2 (x^{2}) + 2 x$ .

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

Step 3.1.5

Factor $2$ out of $2 (x^{2} + x) + 2 \cdot - 6$ .

$\frac{2 (x^{2} + x - 6)}{x + 4}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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 3.2.2

Write the factored form using these integers.

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

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