How do you add or subtract #7/(x-5)-(2+x)/(x-5)#?

1 Answer
Shantelle
Apr 5, 2018

#-1#

Here's how I did it:

Explanation:

To add or subtract fractions, we must have the same denominator for all expressions. In this case, both expressions have the same denominator, #x-5#, so we do not need to worry about that.

This means we can combine the two expressions and just worry about the numerator:
#(7-(2+x))/(x-5)#

Now we distribute the negative to everything in the parenthesis:
#(7-2-x)/(x-5)#

Subtract #7# with #2#:
#(5-x)/(x-5)#

Rewrite that as:
#(-x+5)/(x-5)#

Factor out the negative:
#(-(x-5))/(x-5)#

#(-(cancel(x-5)))/(cancel(x-5))#

#-1#

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