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Factoring the numerator: $4{x}^{2}-12x=4x(x-3)$

Factoring the denominator: $3{x}^{2}+15x=3x(x+5)$

Reducing to lowest terms:

$\begin{array}{rl}{\displaystyle \frac{4{x}^{2}-12x}{3{x}^{2}+15x}}& ={\displaystyle \frac{4\overline{)x}(x-3)}{3\overline{)x}(x+5)}}\\ \\ & ={\displaystyle \frac{4(x-3)}{3(x+5)}}\end{array}$

Finding excluded values: $x\ne -5$