Question

simplify.
\frac{\frac{3x - 6}{2x}}{\frac{9}{x}}

Explanation:

Step1: Rewrite division as multiplication

Dividing by a fraction is multiplying by its reciprocal. So, \(\frac{\frac{3x - 6}{2x}}{\frac{9}{x}}=\frac{3x - 6}{2x}\times\frac{x}{9}\)

Step2: Factor numerator

Factor out 3 from \(3x - 6\): \(3x - 6 = 3(x - 2)\)

Step3: Simplify the expression

Substitute the factored form and cancel common terms. \(\frac{3(x - 2)}{2x}\times\frac{x}{9}=\frac{3(x - 2)\times x}{2x\times9}\). Cancel \(x\) (assuming \(x
eq0\)) and 3: \(\frac{(x - 2)}{2\times3}=\frac{x - 2}{6}\)

Answer:

\(\frac{x - 2}{6}\)