Basic Math Examples

$\frac{\frac{7}{a} + 1}{\frac{7}{a} - 1}$

Step 1

Multiply the numerator and denominator of the fraction by $a$ .

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Step 1.1

Multiply $\frac{\frac{7}{a} + 1}{\frac{7}{a} - 1}$ by $\frac{a}{a}$ .

$\frac{a}{a} \cdot \frac{\frac{7}{a} + 1}{\frac{7}{a} - 1}$

Step 1.2

Combine.

$\frac{a (\frac{7}{a} + 1)}{a (\frac{7}{a} - 1)}$

Step 2

Apply the distributive property.

$\frac{a \frac{7}{a} + a \cdot 1}{a \frac{7}{a} + a \cdot - 1}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $a$ .

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Step 3.1.1

Cancel the common factor.

$\frac{a \frac{7}{a} + a \cdot 1}{a \frac{7}{a} + a \cdot - 1}$

Step 3.1.2

Rewrite the expression.

$\frac{7 + a \cdot 1}{a \frac{7}{a} + a \cdot - 1}$

Step 3.2

Cancel the common factor of $a$ .

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Step 3.2.1

Cancel the common factor.

$\frac{7 + a \cdot 1}{a \frac{7}{a} + a \cdot - 1}$

Step 3.2.2

Rewrite the expression.

$\frac{7 + a \cdot 1}{7 + a \cdot - 1}$

Step 4

Multiply $a$ by $1$ .

$\frac{7 + a}{7 + a \cdot - 1}$

Step 5

Simplify the denominator.

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Step 5.1

Move $- 1$ to the left of $a$ .

$\frac{7 + a}{7 - 1 \cdot a}$

Step 5.2

Rewrite $- 1 a$ as $- a$ .

$\frac{7 + a}{7 - a}$