complex rational expressions?

Question

can someone explain to me in better terms than my book, how we get an answer for:

w+3 over 4w DIVIDED BY w-3 over 2w I am so lost without a teacher in front of me.. I do not recommend online classes without a teacher teaching you math. PLEASE HELP

Answer 1

Given expression
w+3 over 4w DIVIDED BY w-3 over 2w

Solution: ((w+3)/4w) * (2w/(w-3))

Explanation: If you have some rational expression in numerator and denominator then follow these steps:
1. write the rational expression in numerator as it is
i.e. (w+3)/4w
2. multiple the rational expression obtained in above step .1
i.e (w+3)/4w by
the expession obtain by inverting the expression in
denominator i.e. inverting (w-3)/ 2w as 2w/(w-3)
so we get
((w+3)/4w) * (2w/(w-3)) as solution.

Answer 2

Let's see if I can get this right:
[ (w+3) / w] / [ (w-3) / 2w] =
[ (w+3) / w] * [ 2w / (w-3)] =
2w(w+3) / w(w-3) =
2 (w+3) / (w-3)

where w = p + qi, where p and q are rational numbers (from Q).

We could continue, but unless we know where we are going with this, it becomes fruitless.

Answer 3

[(w+3)/(4w)] / [(w-3)/(2w)]

Change to multiplication and flip the 2nd number (multiplication is inverse of division)

[(w+3)/(4w)] * [(2w)/(w-3)]

the (2w)/(4w) = 1/2, so you are left with
(w+3) / [2(w-3)]
(w+3) / (2w-6)