can you get multiple simplified forms?

Question

for the question 6x/2(x+3) ÷ 4x²/5(x+3) - x/2 i got 15-x³/2x² but the answers gave 15-2x²/4x and after testing it with 2 as x i got the same answer so i was wondering if my simplified form also works and what counts as a more simplied form.

Answer 1

(15 - 2x²)/4x is the correct answer. The answer you got is not.

6x/2(x-3) ÷ 4x²/5(x+3) - x/2

= 6x/2(x-3) · 5(x+3)/4x² - x/2 [Invert the denominator (divisor) and multiply]

= 15/4x - x/2

= 15/4x - (x/2)(2x/2x) [Put over common denominator of 4x]

= 15/4x - 2x²/4x

= (15 - 2x²)/4x