Algebra Examples

$\frac{\frac{x}{25} + \frac{x}{5}}{\frac{5}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{x}{25} + \frac{x}{5}) \frac{x}{5}$

Step 2

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

$(\frac{x}{25} + \frac{x}{5} \cdot \frac{5}{5}) \frac{x}{5}$

Step 3

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$(\frac{x}{25} + \frac{x \cdot 5}{5 \cdot 5}) \frac{x}{5}$

Step 3.2

Multiply $5$ by $5$ .

$(\frac{x}{25} + \frac{x \cdot 5}{25}) \frac{x}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{x + x \cdot 5}{25} \cdot \frac{x}{5}$

Step 5

Simplify the numerator.

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Step 5.1

Move $5$ to the left of $x$ .

$\frac{x + 5 \cdot x}{25} \cdot \frac{x}{5}$

Step 5.2

Add $x$ and $5 x$ .

$\frac{6 x}{25} \cdot \frac{x}{5}$

Step 6

Multiply $\frac{6 x}{25} \cdot \frac{x}{5}$ .

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Step 6.1

Multiply $\frac{6 x}{25}$ by $\frac{x}{5}$ .

$\frac{6 x \cdot x}{25 \cdot 5}$

Step 6.2

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

$\frac{6 (x^{1} x)}{25 \cdot 5}$

Step 6.3

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

$\frac{6 (x^{1} x^{1})}{25 \cdot 5}$

Step 6.4

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

$\frac{6 x^{1 + 1}}{25 \cdot 5}$

Step 6.5

Add $1$ and $1$ .

$\frac{6 x^{2}}{25 \cdot 5}$

Step 6.6

Multiply $25$ by $5$ .

$\frac{6 x^{2}}{125}$