Basic Math Examples

$\frac{1}{\frac{7}{c} + 5 - 5}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{1}{\frac{7}{c} + \frac{5 c}{c} - 5}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{\frac{7 + 5 c}{c} - 5}$

Step 1.3

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

$\frac{1}{\frac{7 + 5 c}{c} - 5 \cdot \frac{c}{c}}$

Step 1.4

Combine $- 5$ and $\frac{c}{c}$ .

$\frac{1}{\frac{7 + 5 c}{c} + \frac{- 5 c}{c}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{1}{\frac{7 + 5 c - 5 c}{c}}$

Step 1.6

Reorder terms.

$\frac{1}{\frac{5 c - 5 c + 7}{c}}$

Step 1.7

Rewrite $\frac{5 c - 5 c + 7}{c}$ in a factored form.

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Step 1.7.1

Subtract $5 c$ from $5 c$ .

$\frac{1}{\frac{0 + 7}{c}}$

Step 1.7.2

Add $0$ and $7$ .

$\frac{1}{\frac{7}{c}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{c}{7}$

Step 3

Multiply $\frac{c}{7}$ by $1$ .

$\frac{c}{7}$