How do you combine #(x+2)/(x-5)+(x-12)/(x-5)#?

3 Answers
Mar 16, 2017

#(2x-10)/(x+5)#

Explanation:

#(x+2)/(x-5)##+##(x-12)/(x-5)#

Since both denominators are the same, just combine the fraction, like so,

#((x+2)+(x-12))/(x-5)#

Open up the brackets,

#(x+2+x-12)/(x-5)#
#(2x-10)/(x+5)#

Mar 16, 2017

#2#

Explanation:

Before we can add/subtract fractions we require them to have a #color(blue)"common denominator"#

These fractions have a common denominator ( x - 5) so we can add the numerators, leaving the denominator as it is.

#rArr(x+2+x-12)/(x-5)#

#=(2x-10)/(x-5)#

The numerator can be simplified by taking out a #color(blue)"common factor"#

#rArr(2x-10)/(x-5)=(2(cancel(x-5))^1)/cancel(x-5)^1#

#color(blue)"cancelling" " a common factor of " (x-5)#

#=2#

Mar 16, 2017

#2#

Explanation:

#(x+2)/(x-5)+(x-12)/(x-5)#

#:.=(x+2+x-12)/(x-5)#

#:.=(2x-10)/(x-5)#

#:.=(2cancel((x-5))^color(red)1)/cancel((x-5))^color(red)1#

#:.=2#