A - [AB/(B+C)]= A/[1+B/C]
First, let's replace the denominator on the right hand side with its equivalent [(C + B)/C)
A - [AB/(B + C)]= A/[C + B)/C]
Now, remember that dividing by [(C + B)/C] is the same as multiplying by [C/(C + B)] so that
A - [AB/(B + C)] = [AC/(C + B)]
Now, multiply both sides by (B + C) to get rid of the denominator on the left hand side:
A(B + C) - AB = [AC/(C + B)]*(B + C)
AB + AC - AB = AC
and we are left with
AC = AC which is true. We have, therefore, proven that the two expressions are equivalent.
Also, if you really want to impress your instructor, write the letters QED after your proof. These stand for "Quod erat demonstrandum" (which is what we were trying to prove).