Question

Adding and Subtracting Rational Expressions?
1. (3/x) +(13/x-11)
2. (5/4x^2y)-y/14xz

Please explain how/show work
Thank you :)

Answer 1

Well we need to get common denominators first, so for the first question:
\[\LARGE \frac{3}{x}+\frac{13}{x-11}\]
We need common denominator of x(x-11), so we multiply:
\[\LARGE (\frac{3}{x}*\frac{x-11}{x-11})+(\frac{13}{x-11}*\frac{x}{x})\]
Now just combine and simplify, it'd be best to leave the denominators as they are and distribute the numerator:
\[\LARGE \frac{3x-33}{x(x-11)}+\frac{13x}{x(x-11)}\]
We get:
\[\LARGE \frac{3x-33+13x}{x(x-11)}\]
Simplified:
\[\LARGE \frac{16x-33}{x(x-11)}\]
Hope that made sense :)