# How would I add {5n}/{4n^2-20n} to {5n}/{n-1} (e.g., {5n}/{4n^2-20n}+{5n}/{n-1})?

Feb 19, 2015

When adding two values with different denominators, convert your fractions so they have the same denominator and add the (converted) numerators.

$\frac{5 n}{4 {n}^{2} - 20 n} + \frac{5 n}{n - 1}$

$= \frac{5}{4 n - 20} + \frac{5 n}{n - 1}$

$= \frac{\left(5\right) \cdot \left(n - 1\right)}{\left(4 n - 20\right) \cdot \left(n - 1\right)} + \frac{\left(5 n\right) \cdot \left(4 n - 20\right)}{\left(n - 1\right) \cdot \left(4 n - 20\right)}$

$= \frac{\left(5 n - 5\right) + \left(20 {n}^{2} - 100 n\right)}{4 {n}^{2} - 24 n + 20}$

$= \frac{20 {n}^{2} - 95 n - 5}{4 {n}^{2} - 24 n + 20}$