Algebra Examples

$\frac{y}{x^{3}} + x y$

Step 1

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

$\frac{y}{x^{3}} + \frac{x y x^{3}}{x^{3}}$

Step 2

Combine the numerators over the common denominator.

$\frac{y + x y x^{3}}{x^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $y$ out of $y + x y x^{3}$ .

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Step 3.1.1

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

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

Step 3.1.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1 + x y x^{3}}{x^{3}}$

Step 3.1.3

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

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

Step 3.1.4

Factor $y$ out of $y \cdot 1 + y (x \cdot x^{3})$ .

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

Step 3.2

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 3.2.1

Multiply $x$ by $x^{3}$ .

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Step 3.2.1.1

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

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

Step 3.2.1.2

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

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

Step 3.2.2

Add $1$ and $3$ .

$\frac{y (1 + x^{4})}{x^{3}}$