Question

Can you please help me simplify this into one fraction?

3/(x-3) - 5/(x/2)

Here are the options:
A) -2x+9/(x-3)(x-2)
B) -2x/(x-3)(x-2)
C) -2x-9/(x-3)(x-2)
D) 2x+9/(x-3)(x-2)

I think it's option D but I'm not so sure :(

Answer 1

Typo suspected, corrected version:
3/(x-3) - 5/(x-2)

1. find LCM of denominators
(x-3)(x-2)

2. express both terms in terms of the LCM as denominator
3(x-2)/((x-3)(x-2))-5(x-3)/((x-3)(x-2)) (very similar to cross multiplication)
=(3(x-2)-5(x-3))/((x-3)(x-2))
=(3x-6-5x+15)/((x-3)(x-2))
=(-2x+9)/((x-3)(x-2))

Note:
When writing rational expressions (a polynomial divided by another), it is important to insert parentheses around each of numerator and denominator.
The answers are ALL missing parentheses in the numerator and denominator.
For example, (A) actually means
-2x + 9(x-2)/(x-3), which is far from the intended expression
(-2x+9)/((x-3)(x-2))

Next time, please show your work that you did to come up with choice D.