Pre-Algebra Examples

$\frac{5}{x} + \frac{4}{5 x^{2}}$

Step 1

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

$\frac{5}{x} \cdot \frac{5 x}{5 x} + \frac{4}{5 x^{2}}$

Step 2

Write each expression with a common denominator of $5 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{5}{x}$ by $\frac{5 x}{5 x}$ .

$\frac{5 (5 x)}{x (5 x)} + \frac{4}{5 x^{2}}$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{5 (5 x)}{5 x \cdot x} + \frac{4}{5 x^{2}}$

Step 2.3

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

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Step 2.3.1

Move $x$ .

$\frac{5 (5 x)}{5 (x \cdot x)} + \frac{4}{5 x^{2}}$

Step 2.3.2

Multiply $x$ by $x$ .

$\frac{5 (5 x)}{5 x^{2}} + \frac{4}{5 x^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 (5 x) + 4}{5 x^{2}}$

Step 4

Multiply $5$ by $5$ .

$\frac{25 x + 4}{5 x^{2}}$