Week 15: Adding and Subtracting Rational Expressions

Published by on May 27, 2018 | Leave a response

* In adding and subtracting rational expressions, whether with monomial or polynomial denominators, there are general steps to follow:

  • Identifying the non-permissible value(s)
  • Determine the lowest common denominator (LCD) by factoring the denominators.
  • Rewrite each fraction as a single equivalent fraction with the LCD; be careful with the negative sign when multiplying the numerators by the LCD.
  • Combining the numerators by adding or subtracting.
  • Simplifying if possible: factor the numerator and the denominator to simplify.

* Examples:

  • Monomial denominators:

\frac{4j-5}{3j} + \frac{2j+1}{5j^2} - \frac{7-3j}{2}

The non-permissible value: j \neq 0

->\frac{2(5)j(4j-5) + 3(2)(2j+1) - 3(5) j^2(7-3j)}{3(5)(2) j^2}

->\frac{40 j^2 - 50j +12j +6 -105 j^2 +45 j^3}{30 j^2}

->\frac{45 j^3 - 65 j^2 - 38j + 6}{30 j^2}

  • Polynomial denominators:

\frac{x+2}{x^2 +5x+6} - \frac{2+x}{4- x^2} + \frac{2-x}{x^2 +x-6}

->\frac{x+2}{(x+2)(x+3)} - \frac{2+x}{(2-x)(2+x)} + \frac{- (x-2)}{(x-2)(x+3)}

The non-permissible values: x \neq -2, -3, 2

->\frac{1}{x+3} - \frac{1}{2-x} + \frac{-1}{x+3}

->\frac{1(2-x) - 1(x+3) -(2-x)}{(x+3)(2-x)}

->\frac{2 -x -x -3 -2 +x}{(x+3)(2-x)}

->\frac{-x-3}{(x+3)(2-x)}

->\frac{1}{x-2}

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