Questions: Simplify by removing factors of 1. 5r^2+5r / 10r^2+25r The simplified form is □

Solution Steps

First, we factor the numerator and the denominator of the given expression:

The numerator is \(5r^2 + 5r\). We can factor out a common factor of 5r:

\[ 5r^2 + 5r = 5r(r + 1) \]

The denominator is \(10r^2 + 25r\). We can factor out a common factor of 5r:

\[ 10r^2 + 25r = 5r(2r + 5) \]

Now, substitute the factored forms back into the original expression:

\[ \frac{5r(r + 1)}{5r(2r + 5)} \]

We can cancel the common factor of \(5r\) from the numerator and the denominator:

\[ \frac{r + 1}{2r + 5} \]

Final Answer