How do you combine #4/(a-5) - 1/(5-a)#?

Question

1229 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-02T01:42:42

The combined fraction is #5/(a-5)#.

Rewrite the subtraction as an addition of a negative number:

#color(white)=4/(a-5)-1/(5-a)#

#=4/(a-5)+(-1/(5-a))#

Next, instead of putting that negative sign next to the #1# on the numerator, put it in the denominator, like this:

#color(white)=4/(a-5)+(-1/(5-a))#

#=4/(a-5)+1/(-(5-a))#

Now, just simplify:

#color(white)=4/(a-5)+1/(-(5-a))#

#=4/(a-5)+1/(-5+a)#

#=4/(a-5)+1/(a-5)#

#=(4+1)/(a-5)#

#=5/(a-5)#

This is the simplified answer.