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

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

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

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 $18 = 2 \times 9$ and $99 = 11 \times 9$.
• Step 2: Analyze the variables in the terms $18\frac{ab}{c^2}$ and $-99\frac{c^2}{ab}$.
  Both terms have the fraction form with $\frac{ab}{c^2}$ and $-\frac{c^2}{ab}$.
• Step 3: Identify the common algebraic fraction factor.
  The common factor from the algebraic component is $\frac{ab}{c^2}$.
• Step 4: Factor $\frac{ab}{c^2}$ out from the expression.
  The expression $18\frac{ab}{c^2} - 99\frac{c^2}{ab}$ can be rewritten as:
  $9\frac{ab}{c^2}(2 - 11\frac{c^4}{a^2b^2})$.

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