Question

multiply and simplify.
\\(\frac{40x - 24}{15} cdot \frac{10}{3 - 5x}\\)
\\(\frac{40x - 24}{15} cdot \frac{10}{3 - 5x} = \square\\)
(type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Factor numerator of first fraction

Factor out 8 from \(40x - 24\), we get \(8(5x - 3)\). So the first fraction becomes \(\frac{8(5x - 3)}{15}\). Notice that \(5x - 3 = - (3 - 5x)\), so we can rewrite it as \(\frac{8(-(3 - 5x))}{15}=\frac{-8(3 - 5x)}{15}\).

Step2: Multiply the two fractions

Now multiply \(\frac{-8(3 - 5x)}{15}\) and \(\frac{10}{3 - 5x}\). The \((3 - 5x)\) terms cancel out (assuming \(3 - 5x
eq0\)). We have \(\frac{-8\times10}{15}\).

Step3: Simplify the fraction

Simplify \(\frac{-80}{15}\) by dividing numerator and denominator by 5. \(\frac{-80\div5}{15\div5}=\frac{-16}{3}\).

Answer:

\(-\dfrac{16}{3}\)