Question

sec 1.6 rational expressions. (1 point) simplify this expression. $\frac{t^{5}}{t^{2}-2t}div\frac{1}{t^{2}+2t - 8}=\text{ }$ note: just enter the simplified expression. do not try to enter its re preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining.

Explanation:

Step1: Rewrite division as multiplication

Dividing by a fraction is the same as multiplying by its reciprocal. So, $\frac{t^{5}}{t^{2}-2t}\div\frac{1}{t^{2}+2t - 8}=\frac{t^{5}}{t^{2}-2t}\times(t^{2}+2t - 8)$.

Step2: Factor the denominators and numerators

Factor $t^{2}-2t=t(t - 2)$ and $t^{2}+2t - 8=(t + 4)(t-2)$. Then the expression becomes $\frac{t^{5}}{t(t - 2)}\times(t + 4)(t - 2)$.

Step3: Simplify the expression

Cancel out the common factors $t$ and $(t - 2)$. We get $t^{4}(t + 4)=t^{5}+4t^{4}$.

Answer:

$t^{5}+4t^{4}$