# Complex Fraction

How to solve complex fraction problems: formula, examples, and their solutions.

## Formula

A complex fraction is a fraction

whose numerator or denominator is (are) also fraction(s).

(*a*/*b*) / (*c*/*d*) = (*a*/*b*) ÷ (*c*/*d*) = (*a*/*b*) ⋅ (*d*/*c*).

Dividing rational expressions

So (*a*/*b*) / (*c*/*d*) = *ad*/*bc*.

Multiply the outer factors: *ad*.

Multiply the inner factors: *bc*.

## Example 1

Multiply the outer factors: (*x* + 2)(*x* - 1).

Multiply the inner factors: 7⋅*x*.

## Example 2

Simplify the numerator: 4*a* - 1/*a*.

Factor 4*a*^{2} - 1.

Factoring the difference of squares

To use the formula, change 2*a* + 1 to (2*a* + 1)/1.

Multiply the outer factors: (2*a* + 1)(2*a* - 1)⋅1.

Multiply the inner factors: *a*(2*a* + 1).

Cancel (2*a* + 1).