Question

Two fellow students, Theo and Paula, have added two rational expressions. They ended up at different answers so they have asked you to check their work. Please explain to them any errors that you find.

Answer 1

theo doesn't need to multiply the numerator of the 1st fraction by (x + 2) as it is already over the common denominator (x -5)(x + 2)

the rest of the calculations are correct....

Paula makes her mistake has her mistake in the 5 th line she has incorrectly factored the numerator of the 2nd fraction

she should have collected like terms

\[\frac{2x + 5}{(x-5)(x + 2)} + \frac{x^2 - 4x -5}{(x -5)(x + 2)}\]

collect like terms and you have

\[\frac{2x + 5 + x^2 -4x -5}{(x -5)(x + 2)} = \frac{x^2 -2x}{(x -5)(x +2)}\]

now factor the numerator