Precalculus Examples

$\frac{8 x}{y z} + \frac{4 y}{x z}$

Step 1

To write $\frac{8 x}{y z}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{8 x}{y z} \cdot \frac{x}{x} + \frac{4 y}{x z}$

Step 2

To write $\frac{4 y}{x z}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{8 x}{y z} \cdot \frac{x}{x} + \frac{4 y}{x z} \cdot \frac{y}{y}$

Step 3

Write each expression with a common denominator of $y z x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{8 x}{y z}$ by $\frac{x}{x}$ .

$\frac{8 x \cdot x}{y z x} + \frac{4 y}{x z} \cdot \frac{y}{y}$

Step 3.2

Multiply $\frac{4 y}{x z}$ by $\frac{y}{y}$ .

$\frac{8 x \cdot x}{y z x} + \frac{4 y \cdot y}{x z y}$

Step 3.3

Reorder the factors of $y z x$ .

$\frac{8 x \cdot x}{x y z} + \frac{4 y \cdot y}{x z y}$

Step 3.4

Reorder the factors of $x z y$ .

$\frac{8 x \cdot x}{x y z} + \frac{4 y \cdot y}{x y z}$

Step 4

Combine the numerators over the common denominator.

$\frac{8 x \cdot x + 4 y \cdot y}{x y z}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $4$ out of $8 x \cdot x + 4 y \cdot y$ .

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Step 5.1.1

Factor $4$ out of $8 x \cdot x$ .

$\frac{4 (2 x \cdot x) + 4 y \cdot y}{x y z}$

Step 5.1.2

Factor $4$ out of $4 y \cdot y$ .

$\frac{4 (2 x \cdot x) + 4 (y \cdot y)}{x y z}$

Step 5.1.3

Factor $4$ out of $4 (2 x \cdot x) + 4 (y \cdot y)$ .

$\frac{4 (2 x \cdot x + y \cdot y)}{x y z}$

Step 5.2

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

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Step 5.2.1

Move $x$ .

$\frac{4 (2 (x \cdot x) + y \cdot y)}{x y z}$

Step 5.2.2

Multiply $x$ by $x$ .

$\frac{4 (2 x^{2} + y \cdot y)}{x y z}$

Step 5.3

Multiply $y$ by $y$ .

$\frac{4 (2 x^{2} + y^{2})}{x y z}$