Basic Math Examples

$f + \frac{1}{f} - \frac{5}{f}$

Step 1

Combine the numerators over the common denominator.

$f + \frac{1 - 5}{f}$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Subtract $5$ from $1$ .

$f + \frac{- 4}{f}$

Step 2.2

Move the negative in front of the fraction.

$f - \frac{4}{f}$

Step 3

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

$\frac{f \cdot f}{f} - \frac{4}{f}$

Step 4

Combine the numerators over the common denominator.

$\frac{f \cdot f - 4}{f}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

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

$\frac{f^{1} f - 4}{f}$

Step 5.2

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

$\frac{f^{1} f^{1} - 4}{f}$

Step 5.3

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

$\frac{f^{1 + 1} - 4}{f}$

Step 5.4

Add $1$ and $1$ .

$\frac{f^{2} - 4}{f}$

Step 5.5

Rewrite $4$ as $2^{2}$ .

$\frac{f^{2} - 2^{2}}{f}$

Step 5.6

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = f$ and $b = 2$ .

$\frac{(f + 2) (f - 2)}{f}$