Algebra Examples

${(\frac{3 x}{\frac{1}{x} - 5})}^{- 1}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

${(\frac{3 x}{\frac{1}{x} - 5 \cdot \frac{x}{x}})}^{- 1}$

Step 1.2

Combine $- 5$ and $\frac{x}{x}$ .

${(\frac{3 x}{\frac{1}{x} + \frac{- 5 x}{x}})}^{- 1}$

Step 1.3

Combine the numerators over the common denominator.

${(\frac{3 x}{\frac{1 - 5 x}{x}})}^{- 1}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

${(3 x \frac{x}{1 - 5 x})}^{- 1}$

Step 3

Multiply $3 x \frac{x}{1 - 5 x}$ .

Tap for more steps...

Step 3.1

Combine $3$ and $\frac{x}{1 - 5 x}$ .

${(x \frac{3 x}{1 - 5 x})}^{- 1}$

Step 3.2

Combine $x$ and $\frac{3 x}{1 - 5 x}$ .

${(\frac{x (3 x)}{1 - 5 x})}^{- 1}$

Step 3.3

Raise $x$ to the power of $1$ .

${(\frac{3 (x^{1} x)}{1 - 5 x})}^{- 1}$

Step 3.4

Raise $x$ to the power of $1$ .

${(\frac{3 (x^{1} x^{1})}{1 - 5 x})}^{- 1}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{3 x^{1 + 1}}{1 - 5 x})}^{- 1}$

Step 3.6

Add $1$ and $1$ .

${(\frac{3 x^{2}}{1 - 5 x})}^{- 1}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{1 - 5 x}{3 x^{2}}$