Pre-Algebra Examples

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

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

Step 1

To write

\frac{5}{x}

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

\frac{5 x}{5 x}

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

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

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

Step 2

Write each expression with a common denominator of

5 x^{2}

$5 x^{2}$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 2.1

Multiply

\frac{5}{x}

$\frac{5}{x}$ by

\frac{5 x}{5 x}

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

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

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

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

Step 2.3

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.3.1

Move

x

$x$ .

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

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

Step 2.3.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

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

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

Step 3

Combine the numerators over the common denominator.

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

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

Step 4

Multiply

5

$5$ by

5

$5$ .

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

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

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

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

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