Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{1}{x^{2}} + \frac{1}{x} \cdot \frac{x}{x}) x^{3}$

Step 3

Write each expression with a common denominator of $x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{x}$ by $\frac{x}{x}$ .

$(\frac{1}{x^{2}} + \frac{x}{x \cdot x}) x^{3}$

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{1 + x}{x^{2}} x^{3}$

Step 5

Cancel the common factor of $x^{2}$ .

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Step 5.1

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

$\frac{1 + x}{x^{2}} (x^{2} x)$

Step 5.2

Cancel the common factor.

$\frac{1 + x}{x^{2}} (x^{2} x)$

Step 5.3

Rewrite the expression.

$(1 + x) x$

Step 6

Apply the distributive property.

$1 x + x \cdot x$

Step 7

Simplify the expression.

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Step 7.1

Multiply $x$ by $1$ .

$x + x \cdot x$

Step 7.2

Multiply $x$ by $x$ .

$x + x^{2}$