Question

perform the indicated operation and simplify please help.

(v-5)/(v-6)-(v+1)/(v+6)+(v-18)/(v^2-36)

Answer 1

Notice that the denominator consists of
(v-6), (v+6), and (v^2-36)=(v+6)(v-6)

Therefore the common denominator is
(v²-36)=(v+6)(v-6)

The first fraction becomes:
(v-5)(v+6)
-------------
(v²-36)

The second fraction becomes:
(v+1)(v-6)
-------------
(v²-36)

And the third one stays at:
(v-18)
-------------
(v²-36)

Since we have a common denominator, we can expand the numberators and add to get:

7(v-6)
---------
(v+6)(v-6)
which after cancelling gives:
7/(v+6).