11 Unlike Denominators Determine the LCD. Rewrite each fraction as an equivalent fraction with the LCD.Add or subtract the numerators while maintaining the LCD.When possible, factor the remaining numerator and simplify the fraction.
12 Unlike DenominatorsExample:a.)The LCD is w(w+2).
13 This cannot be factored any further. Unlike DenominatorsExample:b.)The LCD is 12x(x – 1).This cannot be factored any further.
15 Simplifying Complex Fractions A complex fraction is one that has a fraction in its numerator or its denominator or in both the numerator and denominator.Example:
16 So how can we simplify them? Remember, fractions are just division problems.We can rewrite the complex fraction as a division problem with two fractions.This division problem then changes to multiplication by the reciprocal.
17 Simplifying Complex Fractions Rule Any complex fractionWhere b ≠ 0, c ≠ 0, and d ≠ 0, may be expressed as:
18 What if we have mixed numbers in the complex fraction? If we have mixed numbers, we treat it as an addition problem with unlike denominators.We want to be working with two fractions, so make sure the numerator is one fraction, and the denominator is one fractionNow we can rewrite the complex fraction as a division of two fractions
21 What about complex rational expression? Treat the complex rational expression as a division problemAdd any rational expressions to form rational expressions in the numerator and denominatorFactorSimplify“Bad” values
22 Ex. 2: Simplify← The LCD is xy for both the numerator and the denominator.← Add to simplify the numerator and subtract to simplify the denominator.← Multiply the numerator by the reciprocal of the denominator.