Question

simplify the expression.
\frac{\frac{6}{x + y}-\frac{6}{x}}{y}
\frac{\frac{6}{x + y}-\frac{6}{x}}{y}=\square

Explanation:

Step1: Find common denominator for numerator

First, find a common - denominator for $\frac{6}{x + y}-\frac{6}{x}$. The common denominator is $x(x + y)$. So, $\frac{6}{x + y}-\frac{6}{x}=\frac{6x-6(x + y)}{x(x + y)}=\frac{6x-6x-6y}{x(x + y)}=\frac{-6y}{x(x + y)}$.

Step2: Divide by $y$

Now, we have $\frac{\frac{-6y}{x(x + y)}}{y}$. When dividing by a number is the same as multiplying by its reciprocal. So, $\frac{-6y}{x(x + y)}\times\frac{1}{y}=\frac{-6}{x(x + y)}$.

Answer:

$\frac{-6}{x(x + y)}$