Algebra Examples

$\frac{- 6 x^{2} + x - 3}{x^{2} + 9} - \frac{- 2 x - 4}{x^{2} + 9}$

Step 1

Combine the numerators over the common denominator.

$\frac{- 6 x^{2} + x - 3 - (- 2 x - 4)}{x^{2} + 9}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{- 6 x^{2} + x - 3 - (- 2 x) - - 4}{x^{2} + 9}$

Step 2.2

Multiply $- 2$ by $- 1$ .

$\frac{- 6 x^{2} + x - 3 + 2 x - - 4}{x^{2} + 9}$

Step 2.3

Multiply $- 1$ by $- 4$ .

$\frac{- 6 x^{2} + x - 3 + 2 x + 4}{x^{2} + 9}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Add $x$ and $2 x$ .

$\frac{- 6 x^{2} + 3 x - 3 + 4}{x^{2} + 9}$

Step 3.2

Add $- 3$ and $4$ .

$\frac{- 6 x^{2} + 3 x + 1}{x^{2} + 9}$

Step 3.3

Factor $- 1$ out of $- 6 x^{2}$ .

$\frac{- (6 x^{2}) + 3 x + 1}{x^{2} + 9}$

Step 3.4

Factor $- 1$ out of $3 x$ .

$\frac{- (6 x^{2}) - (- 3 x) + 1}{x^{2} + 9}$

Step 3.5

Factor $- 1$ out of $- (6 x^{2}) - (- 3 x)$ .

$\frac{- (6 x^{2} - 3 x) + 1}{x^{2} + 9}$

Step 3.6

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

$\frac{- (6 x^{2} - 3 x) - 1 (- 1)}{x^{2} + 9}$

Step 3.7

Factor $- 1$ out of $- (6 x^{2} - 3 x) - 1 (- 1)$ .

$\frac{- (6 x^{2} - 3 x - 1)}{x^{2} + 9}$

Step 3.8

Simplify the expression.

Tap for more steps...

Step 3.8.1

Rewrite $- (6 x^{2} - 3 x - 1)$ as $- 1 (6 x^{2} - 3 x - 1)$ .

$\frac{- 1 (6 x^{2} - 3 x - 1)}{x^{2} + 9}$

Step 3.8.2

Move the negative in front of the fraction.

$- \frac{6 x^{2} - 3 x - 1}{x^{2} + 9}$