How do you simplify \frac { x ^ { 2} + 17x } { x ^ { 2} - 5x } + \frac { x ^ { 2} - 6x } { x ^ { 2} - 5x }?

2 Answers
Nov 1, 2017

(2x+11)/(x-5)

Explanation:

x^2-5x!=0=>x (x-5)!=0=>x!=0 and x-5!=0
" "
=>x!=0 and x!=5
" "
(x^2+17x)/(x^2-5x)+(x^2-6x)/(x^2-5x)
" "
=(x^2+17x+x^2-6x)/(x^2-5x)
" "
=(x^2+x^2+17x-6x)/(x^2-5x)
" "
=(2x^2+11x)/(x^2-5x)
" "
=(x (2x+11))/(x (x-5))
" "
=(2x+11)/(x-5)

Nov 1, 2017

(2x+11)/(x+5)

Explanation:

First - common factor out x. Then we have:
[x(x+17)]/[x(x-5)]+[x(x-6)]/[x(x-5)]

Now you can 'cross out' or 'cancel out' the x variables outside the brackets. Now we have:
(x+17)/(x-5)+(x-6)/(x-5)

Now you can collect like terms:
(2x+11)/(x+5)