How do you subtract #\frac { 3} { a - 2} + \frac { 5} { 2- a }#?

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Answer 1 · 2017-08-29T01:21:33

#3/(a-2)-5/(a-2)=-2/(a-2)#

Let's look at the denominators #a-2# and #2-a#. Notice that:

#a-2=-(-2+a)=-(a-2)#

And so we can rewrite the expression:

#3/(a-2)+5/(2-a)#

#3/(a-2)+5/(-(a-2))#

Keep in mind that I can move that negative sign can be moved!

#color(red)(-1/2=(-1)/2=1/(-2)#

or, more generally,

#color(red)(-a/b=(-a)/b=a/(-b)#

and so I can rewrite our expression:

#3/(a-2)+5/(-(a-2))#

#3/(a-2)-5/(a-2)#

and now we can subtract:

#3/(a-2)-5/(a-2)=-2/(a-2)#