How do you combine #3/(b-3)-b/(b-3)#?

3 Answers
May 19, 2015

When you have the sum or subtraction of two fraction with the same denominator you simply mantain that denominator and sum/subtract the numerators:
#(3-b)/(b-3)=-(b-3)/(b-3)=-1#
I changed the sign by collecting #-1# on the numerator.

May 19, 2015

#3/(b - 3) - b/(b - 3) = (-(b - 3))/(b - 3) = -1#

May 19, 2015

When you have a sum or subtraction of fractions that share the same denominator, you can simply add/subtract the numerators, as follows:

#3/(b-3)-b/(b-3)=(3-b)/(b-3)#

Note that the numerator and the denominator are opposite, that is, one is the negative version of the other:

#(3-b)(-1)=(b-3)#, thus #(3-b)=-(b-3)#
and
#(b-3)(-1)=(3-b)#, thus #(b-3)=-(3-b)#

Thus, we can either rewrite it as

#((3-b)(-1))/(b-3)=(-(b-3))/(b-3)=-1#

or

#(3-b)/((b-3)(-1))=(3-b)/(-(3-b))=-1#

So, the final and shortest answer for your subtraction is #-1#