SOLUTION: I need to simplify each complex fraction. Please help this is confusing. (w+3)/4w divided by(w-3)/2w

Algebra ->  Expressions-with-variables -> SOLUTION: I need to simplify each complex fraction. Please help this is confusing. (w+3)/4w divided by(w-3)/2w      Log On


   



Question 119455: I need to simplify each complex fraction. Please help this is confusing.
(w+3)/4w divided by(w-3)/2w

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28w%2B3%29%2F4w%29%2F%28%28w-3%29%2F2w%29

Remember the rule for dividing one fraction by another: Invert the denominator fraction and multiply:

%28p%2Fq%29%2F%28r%2Fs%29=%28p%2Fq%29%28s%2Fr%29 for all real p, q, r, and s, so

%28%28w%2B3%29%2F4w%29%2F%28%28w-3%29%2F2w%29=%28%28w%2B3%29%2F4w%29%282w%2F%28w-3%29%29

Now you just multiply the numerators and the denominators the same way you would multiply any other two fractions:

%28%28w%2B3%29%2F4w%29%282w%2F%28w-3%29%29=%282w%28w%2B3%29%29%2F%284w%28w-3%29%29

Since there is a factor of 2w in both the numerator and denominator, we can eliminate that, so:

%282w%28w%2B3%29%29%2F%284w%28w-3%29%29=%28w%2B3%29%2F%282%28w-3%29%29

Since there are no more common factors in the numerator and denominator, we are done except for distributing the 2 in the denominator across the (w - 3) to remove the parentheses, thus:

%28w%2B3%29%2F%282w-6%29

Let's check our work:

We know that if p%2Fq=r then rq=p, so if %28%28w%2B3%29%2F4w%29%2F%28%28w-3%29%2F2w%29=%28w%2B3%29%2F%282w-6%29, then %28%28w-3%29%2F2w%29%28%28w%2B3%29%2F%282w-6%29%29=%28w%2B3%29%2F4w must be true.



Now factor a 2 out of the binomial in the denominator resulting in:

%28%28w-3%29%28w%2B3%29%29%2F4w%28w-3%29=%28w%2B3%29%2F4w once you eliminate the common factor of (w - 3), and that verifies the answer.

Hope that helps.
John