Calculus Examples

$\frac{1 - \frac{2 x}{3 x - 4}}{x + \frac{32}{3 x - 4}}$

Step 1

Multiply the numerator and denominator of the fraction by $3 x - 4$ .

Tap for more steps...

Step 1.1

Multiply $\frac{1 - \frac{2 x}{3 x - 4}}{x + \frac{32}{3 x - 4}}$ by $\frac{3 x - 4}{3 x - 4}$ .

$\frac{3 x - 4}{3 x - 4} \cdot \frac{1 - \frac{2 x}{3 x - 4}}{x + \frac{32}{3 x - 4}}$

Step 1.2

Combine.

$\frac{(3 x - 4) (1 - \frac{2 x}{3 x - 4})}{(3 x - 4) (x + \frac{32}{3 x - 4})}$

Step 2

Apply the distributive property.

$\frac{(3 x - 4) \cdot 1 + (3 x - 4) (- \frac{2 x}{3 x - 4})}{(3 x - 4) x + (3 x - 4) \frac{32}{3 x - 4}}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $3 x - 4$ .

Tap for more steps...

Step 3.1.1

Move the leading negative in $- \frac{2 x}{3 x - 4}$ into the numerator.

$\frac{(3 x - 4) \cdot 1 + (3 x - 4) \frac{- 2 x}{3 x - 4}}{(3 x - 4) x + (3 x - 4) \frac{32}{3 x - 4}}$

Step 3.1.2

Cancel the common factor.

$\frac{(3 x - 4) \cdot 1 + (3 x - 4) \frac{- 2 x}{3 x - 4}}{(3 x - 4) x + (3 x - 4) \frac{32}{3 x - 4}}$

Step 3.1.3

Rewrite the expression.

$\frac{(3 x - 4) \cdot 1 - 2 x}{(3 x - 4) x + (3 x - 4) \frac{32}{3 x - 4}}$

Step 3.2

Cancel the common factor of $3 x - 4$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{(3 x - 4) \cdot 1 - 2 x}{(3 x - 4) x + (3 x - 4) \frac{32}{3 x - 4}}$

Step 3.2.2

Rewrite the expression.

$\frac{(3 x - 4) \cdot 1 - 2 x}{(3 x - 4) x + 32}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $3 x - 4$ by $1$ .

$\frac{3 x - 4 - 2 x}{(3 x - 4) x + 32}$

Step 4.2

Subtract $2 x$ from $3 x$ .

$\frac{x - 4}{(3 x - 4) x + 32}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{x - 4}{3 x \cdot x - 4 x + 32}$

Step 5.2

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

Tap for more steps...

Step 5.2.1

Move $x$ .

$\frac{x - 4}{3 (x \cdot x) - 4 x + 32}$

Step 5.2.2

Multiply $x$ by $x$ .

$\frac{x - 4}{3 x^{2} - 4 x + 32}$