Question

simplify.
\\(\dfrac{\dfrac{3x - 12}{x}}{\dfrac{15}{4x}}\\)

Explanation:

Step1: Rewrite as multiplication

Dividing by a fraction is multiplying by its reciprocal. So, \(\frac{\frac{3x - 12}{x}}{\frac{15}{4x}}=\frac{3x - 12}{x}\times\frac{4x}{15}\)

Step2: Factor numerator

Factor \(3\) from \(3x - 12\): \(3x - 12 = 3(x - 4)\)
Now the expression is \(\frac{3(x - 4)}{x}\times\frac{4x}{15}\)

Step3: Cancel common factors

Cancel \(x\) (since \(x
eq0\)) and simplify \(3\) and \(15\) (divide numerator and denominator by \(3\)):
\(\frac{3(x - 4)}{x}\times\frac{4x}{15}=\frac{(x - 4)\times4}{5}\)

Step4: Multiply out

\(\frac{4(x - 4)}{5}=\frac{4x - 16}{5}\)

Answer:

\(\frac{4x - 16}{5}\) (or \(\frac{4(x - 4)}{5}\))