Finite Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Subtract $x$ from $x$ .

$\frac{- 3 x^{2} - 6 h x - 3 h^{2} + 0 - h}{h}$

Step 1.3

Add $- 3 x^{2}$ and $0$ .

$\frac{- 3 x^{2} - 6 h x - 3 h^{2} - h}{h}$

Step 2

Simplify with factoring out.

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Step 2.1

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

$\frac{- (3 x^{2}) - 6 h x - 3 h^{2} - h}{h}$

Step 2.2

Factor $- 1$ out of $- 6 h x$ .

$\frac{- (3 x^{2}) - (6 h x) - 3 h^{2} - h}{h}$

Step 2.3

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

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

Step 2.4

Factor $- 1$ out of $- 3 h^{2}$ .

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

Step 2.5

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

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

Step 2.6

Factor $- 1$ out of $- h$ .

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

Step 2.7

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

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

Step 2.8

Simplify the expression.

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Step 2.8.1

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

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

Step 2.8.2

Move the negative in front of the fraction.

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