explain how to add rational expressions

Answer 1

same as you do with ordinary numeric fractions. Find a common denominator and use that to combine them.

(x-2)/(x+3) + (2x-7)/(x-5) - 3/(x-2)

Common denominator is (x+3)(x-5)(x-2). So, now you can multiply each term by the needed factors:

(x-2)(x-5)(x-2) + (2x-7)(x+3)(x-2) - 3(x+3)(x-5)
-------------------------------------------------------------
(x+3)(x-5)(x-2)

3x^3-17x^2+11x+67
----------------------------
(x+3)(x-5)(x-2)

Answer 2

Thank you so much!