Complex Fraction

Complex Fraction

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

Formula

(a/b)/(c/d) = ad/bc

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

Simplify the given expression. ((x + 2)/x)/(7/(x - 1))

Multiply the outer factors: (x + 2)(x - 1).
Multiply the inner factors: 7⋅x.

Example 2

Simplify the given expression. (4a - 1/a)/(2a + 1)

Simplify the numerator: 4a - 1/a.

Factor 4a2 - 1.
Factoring the difference of squares

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

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

Cancel (2a + 1).