Factor GCF from numerator: Factor out the greatest common factor (GCF) from the numerator -12t^2 - 18t. The GCF of -12t^2 and -18t is -6t. So we factor -6t out of the numerator. -12t^2 - 18t = -6t(2t + 3)Factor GCF from denominator: Factor out the greatest common factor (GCF) from the denominator 8t^2 + 18t. The GCF of 8t^2 and 18t is 2t. So we factor 2t out of the denominator. 8t^2 + 18t = 2t(4t + 9)Rewrite with factored terms: Rewrite the expression with the factored numerator and denominator. The expression now looks like this: (-6t(2t + 3))/(2t(4t + 9))Cancel common 't' term: Cancel out the common t term from the numerator and denominator. Since t is a common factor in both the numerator and the denominator, we can cancel it out, but we must be careful to not cancel it if t = 0 because division by zero is undefined. The expression simplifies to: (-6(2t + 3))/(2(4t + 9))Simplify by canceling factors: Simplify the expression by canceling out any common numerical factors. We notice that -6 and 2 have a common factor of 2. Dividing both by 2 gives us: (-3(2t + 3))/(1(4t + 9)) Which simplifies to: -3(2t + 3)/(4t + 9)

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$\frac{-12t^2 - 18t}{8t^2 + 18}$

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\frac{-12t^2 - 18t}{8t^2 + 18}

Factor GCF from numerator: Factor out the greatest common factor (GCF) from the numerator $-12t^2 - 18t$ . $\newline$ The GCF of $-12t^2$ and $-18t$ is $-6t$ . So we factor $-6t$ out of the numerator. $\newline$ $-12t^2 - 18t = -6t(2t + 3)$
Factor GCF from denominator: Factor out the greatest common factor (GCF) from the denominator $8t^2 + 18t$ . The GCF of $8t^2$ and $18t$ is $2t$ . So we factor $2t$ out of the denominator. $8t^2 + 18t = 2t(4t + 9)$
Rewrite with factored terms: Rewrite the expression with the factored numerator and denominator. $\newline$ The expression now looks like this: $\newline$ $(-6t(2t + 3))/(2t(4t + 9))$
Cancel common 't' term: Cancel out the common $t$ term from the numerator and denominator. $\newline$ Since $t$ is a common factor in both the numerator and the denominator, we can cancel it out, but we must be careful to not cancel it if $t = 0$ because division by zero is undefined. $\newline$ The expression simplifies to: $\newline$ $(-6(2t + 3))/(2(4t + 9))$
Simplify by canceling factors: Simplify the expression by canceling out any common numerical factors. $\newline$ We notice that $-6$ and $2$ have a common factor of $2$ . Dividing both by $2$ gives us: $\newline$ $(-3(2t + 3))/(1(4t + 9))$ $\newline$ Which simplifies to: $\newline$ $-3(2t + 3)/(4t + 9)$