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Least common denominator of rational expressions worksheets Grades 9–10

Find the LCD of algebraic fractions by factoring each denominator.

The front of the free least common denominator of rational expressions worksheet
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Free · Worked example · 17 problems · Answer key · US Letter

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How to do it

Factor each denominator. The LCD uses the LCM of the numbers and every factor at its highest power. Leave it factored.

2(x+7)(x+6),1(x+7)(x−5)LCD =(x+7)(x+6)(x−5)\dfrac{2}{(x + 7)(x + 6)},\quad \dfrac{1}{(x + 7)(x - 5)}\quad \text{LCD }= (x + 7)(x + 6)(x - 5)
LCD =(x+7)(x+6)(x−5)\text{LCD }= (x + 7)(x + 6)(x - 5)each factor once, at its highest power

Example problems

  1. 94x(x+4),56(x+4)2LCD =\dfrac{9}{4x(x + 4)},\quad \dfrac{5}{6(x + 4)^{2}}\quad \text{LCD }=
  2. 53x(x+6),76(x+6)2LCD =\dfrac{5}{3x(x + 6)},\quad \dfrac{7}{6(x + 6)^{2}}\quad \text{LCD }=
  3. 1(x−3)(x−2),1(x−3)(x+1)LCD =\dfrac{1}{(x - 3)(x - 2)},\quad \dfrac{1}{(x - 3)(x + 1)}\quad \text{LCD }=
  4. 56x3,74xLCD =\dfrac{5}{6x^{3}},\quad \dfrac{7}{4x}\quad \text{LCD }=

Rational expressions and equations

  1. Adding and subtracting rational expressions with like denominators
  2. Least common denominator of rational expressions
  3. Adding rational expressions with unlike denominators
  4. Subtracting rational expressions with unlike denominators
  5. Adding and subtracting rational expressions by factoring
  6. Simplifying complex fractions
  7. Solving rational proportions
  8. Solving rational equations