Decompose the Expression: 18ab/c² - 99c²/ab

Question

Which of the expressions is a decomposition of the expression below?

18abc299c2ab 18\frac{ab}{c^2}-99\frac{c^2}{ab}

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Determine the greatest common divisor (GCD) of the numeric coefficients 18 and 99.
    The GCD of 18 and 99 is 9 since 18=2×918 = 2 \times 9 and 99=11×999 = 11 \times 9.
  • Step 2: Analyze the variables in the terms 18abc218\frac{ab}{c^2} and 99c2ab-99\frac{c^2}{ab}.
    Both terms have the fraction form with abc2\frac{ab}{c^2} and c2ab-\frac{c^2}{ab}.
  • Step 3: Identify the common algebraic fraction factor.
    The common factor from the algebraic component is abc2\frac{ab}{c^2}.
  • Step 4: Factor abc2\frac{ab}{c^2} out from the expression.
    The expression 18abc299c2ab18\frac{ab}{c^2} - 99\frac{c^2}{ab} can be rewritten as:
    9abc2(211c4a2b2)9\frac{ab}{c^2}(2 - 11\frac{c^4}{a^2b^2}).

Therefore, the decomposition of the given expression is 9abc2(211c4a2b2)9\frac{ab}{c^2}(2 - 11\frac{c^4}{a^2b^2}).

Answer

9abc2(211c4a2b2) 9\frac{ab}{c^2}(2-11\frac{c^4}{a^2b^2})