# How do you multiply (t^2+5t)/(t+1)div(t+5)?

$\frac{t}{t + 1}$

#### Explanation:

With the statement $\frac{{t}^{2} + 5 t}{t + 1} \div \left(t + 5\right)$, let's first see that we can factor the numerator on the left-hand side. The other thing to notice is that when we have something in the form of $\frac{a}{b} \div \frac{c}{d}$, it can be restated as $\frac{a}{b} \times \frac{d}{c}$, and so:

$\frac{{t}^{2} + 5 t}{t + 1} \div \frac{t + 5}{1}$

$\frac{t \left(t + 5\right)}{t + 1} \times \frac{1}{t + 5}$

And now we can cancel:

$\frac{t \left(\cancel{t + 5}\right)}{t + 1} \times \frac{1}{\cancel{t + 5}}$

$\frac{t}{t + 1}$