For t!=0, which of the following expressions is equivalent to (-12t^(2)-18 t)/(8t^(2)+18 t) ? Choose 1 answer: (A) (6t+9)/(4t+9) (B) (-6t+9)/(4t+9) (C) (-6t-1)/(4t+1) (D) (-6t-9)/(4t+9)

Factor GCF: Factor out the greatest common factor from the numerator and the denominator. The greatest common factor of the numerator (-12t^2 - 18t) is 6t, and for the denominator (8t^2 + 18t) is 2t.Factor Numerator & Denominator: Factor the greatest common factor from the numerator and the denominator. Numerator: -12t^2 - 18t = -6t(2t + 3) Denominator: 8t^2 + 18t = 2t(4t + 9)Cancel Common Factor: Simplify the expression by canceling out the common factor of t from the numerator and the denominator. (-6t(2t + 3))/(2t(4t + 9)) = (-6(2t + 3))/(2(4t + 9))Further Simplify: Simplify the expression further by canceling out the common factor of 2 from the numerator and the denominator. (-6(2t + 3))/(2(4t + 9)) = (-3(2t + 3))/(4t + 9)Distribute -3: Distribute the -3 in the numerator. (-3(2t + 3))/(4t + 9) = (-6t - 9)/(4t + 9)

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Math Problems

Algebra 2

Simplify rational expressions

Full solution

Q. For

t\neq 0

, which of the following expressions is equivalent to

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

\newline

Choose

1

answer:

\newline

(A)

\frac{6t+9}{4t+9}

\newline

(B)

\frac{-6t+9}{4t+9}

\newline

(C)

\frac{-6t-1}{4t+1}

\newline

(D)

\frac{-6t-9}{4t+9}

Factor GCF: Factor out the greatest common factor from the numerator and the denominator. $\newline$ The greatest common factor of the numerator $-12t^2 - 18t$ is $6t$ , and for the denominator $8t^2 + 18t$ is $2t$ .
Factor Numerator & Denominator: Factor the greatest common factor from the numerator and the denominator. $\newline$ Numerator: $-12t^2 - 18t = -6t(2t + 3)$ $\newline$ Denominator: $8t^2 + 18t = 2t(4t + 9)$
Cancel Common Factor: Simplify the expression by canceling out the common factor of $t$ from the numerator and the denominator. $\frac{-6t(2t + 3)}{2t(4t + 9)} = \frac{-6(2t + 3)}{2(4t + 9)}$
Further Simplify: Simplify the expression further by canceling out the common factor of $2$ from the numerator and the denominator. $\frac{-6(2t + 3)}{2(4t + 9)} = \frac{-3(2t + 3)}{4t + 9}$
Distribute $-3$ : Distribute the $-3$ in the numerator. $\newline$ $\frac{-3(2t + 3)}{4t + 9} = \frac{-6t - 9}{4t + 9}$