simplify complex fraction?

Question

w+3/4w / w-3/2w

Answer 1

w+3/4w / w-3/2w

invert and multiply

w+3/4w * 2w / w-3 2w is 1 and 4w is 2

w+3 / 2(w-3)

Answer 2

This is (w+3)/4w /(w-3)/2w: correct? If it is then this is
one fraction being divided by another.
To simplify this, invert the bottom fraction, and multiply
instead of divide. You get
(w+3)/4w X 2w/(w-3), = (w+3)/2(w-3)

What I want to do is show you WHY this rule works.
Let's take a simpler example: a/b / c/d
If I were to multiply a/b /c/d by 1, it's no big deal, is it.
a/b /c/d X 1=a/b / c/d.
Even if I wrote 1 as 1/1, it's still no big deal:
a/b / c/d X 1/1=a/b /c/d.
What if I wrote 1/1 as d/c / d/c? Well d/c / d/c is most
certainly =1, but look what happens to my division
problem.
a/b /c/d X d/c /d/c=a/d X d/c /c/d X d/c.
Please recopy this so that the fractions and division
lines are all vertical. It's much clearer that way.
By making 1= d/c /d/c, the denominator of the
original division problem "disappears" because
c/d X d/c =1. You're left with (a/b X d/c) /1, which is
simply a/b X d/c.
In effect, you go from start to finish by a short-cut:
turn the denominator upside-down, and multiply it
and the original numerator together!
You can now use this short-cut whenever you want.
When dividing one fraction by another,it works every
time.
One final tip. 2 /3/4 fits this rule.
2 is 2/1, so you have 2/1 / 3/4, =2/1 X 4/3, =8/3

Answer 3

Its hard to read an equation like this if you don't group terms together using brackets, so I might have read your question wrong.

Remember the keep change flip operation....

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

keep the top term the same and flip the denominator and multiply the top and the newly flipped terms together.

ie.

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

= (w+3) / (2w-6)