Finite Math Examples

$\frac{\frac{8 x + 8 h + 3}{x + h} - 8 x + 3}{h}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

To write $- 8 x$ as a fraction with a common denominator, multiply by $\frac{x + h}{x + h}$ .

$\frac{\frac{8 x + 8 h + 3}{x + h} - 8 x \cdot \frac{x + h}{x + h} + 3}{h}$

Step 1.2

Combine $- 8 x$ and $\frac{x + h}{x + h}$ .

$\frac{\frac{8 x + 8 h + 3}{x + h} + \frac{- 8 x (x + h)}{x + h} + 3}{h}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{\frac{8 x + 8 h + 3 - 8 x (x + h)}{x + h} + 3}{h}$

Step 1.4

To write $3$ as a fraction with a common denominator, multiply by $\frac{x + h}{x + h}$ .

$\frac{\frac{8 x + 8 h + 3 - 8 x (x + h)}{x + h} + \frac{3 (x + h)}{x + h}}{h}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{\frac{8 x + 8 h + 3 - 8 x (x + h) + 3 (x + h)}{x + h}}{h}$

Step 1.6

Rewrite $\frac{8 x + 8 h + 3 - 8 x (x + h) + 3 (x + h)}{x + h}$ in a factored form.

Tap for more steps...

Step 1.6.1

Apply the distributive property.

$\frac{\frac{8 x + 8 h + 3 - 8 x \cdot x - 8 x h + 3 (x + h)}{x + h}}{h}$

Step 1.6.2

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

Tap for more steps...

Step 1.6.2.1

Move $x$ .

$\frac{\frac{8 x + 8 h + 3 - 8 (x \cdot x) - 8 x h + 3 (x + h)}{x + h}}{h}$

Step 1.6.2.2

Multiply $x$ by $x$ .

$\frac{\frac{8 x + 8 h + 3 - 8 x^{2} - 8 x h + 3 (x + h)}{x + h}}{h}$

Step 1.6.3

Apply the distributive property.

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

Step 1.6.4

Add $8 x$ and $3 x$ .

$\frac{\frac{8 h + 3 - 8 x^{2} - 8 x h + 11 x + 3 h}{x + h}}{h}$

Step 1.6.5

Add $8 h$ and $3 h$ .

$\frac{\frac{11 h + 3 - 8 x^{2} - 8 x h + 11 x}{x + h}}{h}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{11 h + 3 - 8 x^{2} - 8 x h + 11 x}{x + h} \cdot \frac{1}{h}$

Step 3

Multiply $\frac{11 h + 3 - 8 x^{2} - 8 x h + 11 x}{x + h}$ by $\frac{1}{h}$ .

$\frac{11 h + 3 - 8 x^{2} - 8 x h + 11 x}{(x + h) h}$

Step 4

Reorder factors in $\frac{11 h + 3 - 8 x^{2} - 8 x h + 11 x}{(x + h) h}$ .

$\frac{11 h + 3 - 8 x^{2} - 8 x h + 11 x}{h (x + h)}$