Question

simplify the rational expression.\\(\frac{-4m^2 + 8m}{-4m^2 + 16m}\\)\
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simplify the rational expression.\\(\frac{45x^2 + 9x}{-9x^2 + 27x}\\)

Explanation:

Step1: Factor numerator (first expr)

$\frac{-4m(m - 2)}{-4m^2+16m}$

Step2: Factor denominator (first expr)

$\frac{-4m(m - 2)}{-4m(m - 4)}$

Step3: Cancel common factors (first expr)

$\frac{m-2}{m-4}$

Step4: Factor numerator (second expr)

$\frac{9x(5x + 1)}{-9x^2+27x}$

Step5: Factor denominator (second expr)

$\frac{9x(5x + 1)}{-9x(x - 3)}$

Step6: Cancel common factors (second expr)

$\frac{5x+1}{-x+3}$

Answer:

1. $\frac{m-2}{m-4}$ (where $m

eq 0, 4$)

1. $\frac{5x+1}{-x+3}$ (where $x

eq 0, 3$)