Question

select the correct answer.
it takes austin 8 hours longer than elliott to cons
in 3 hours. this situation can be represented by
$\frac{3}{t} + \frac{3}{t + 8}$
which expression is equivalent to the expression
a. $\frac{6}{t^2 + 8t}$
b. $\frac{6t + 11}{t^2 + 8t}$
c. $\frac{6t + 24}{t^2 + 8t}$
d. $\frac{6}{2t + 8}$

Explanation:

Step1: Find common denominator

The common denominator of $\frac{3}{t}$ and $\frac{3}{t+8}$ is $t(t+8) = t^2+8t$.

Step2: Rewrite fractions with common denominator

$\frac{3(t+8)}{t^2+8t} + \frac{3t}{t^2+8t}$

Step3: Expand numerator terms

$\frac{3t+24}{t^2+8t} + \frac{3t}{t^2+8t}$

Step4: Combine numerators

$\frac{3t+24+3t}{t^2+8t} = \frac{6t+24}{t^2+8t}$

Answer:

C. $\frac{6t + 24}{t^2 + 8t}$