SOLUTION: Simplify the complex fraction. (a/b+c)/(a/b-c)= ? (1/4+x)/(1/2)= ? (1/3+1/5-1/7)/(1/x)= ? (a/b+2+b/a)/(a/b-b/a)= ?

Algebra ->  Expressions-with-variables -> SOLUTION: Simplify the complex fraction. (a/b+c)/(a/b-c)= ? (1/4+x)/(1/2)= ? (1/3+1/5-1/7)/(1/x)= ? (a/b+2+b/a)/(a/b-b/a)= ?       Log On


   

Question 203264: Simplify the complex fraction.
(a/b+c)/(a/b-c)= ?
(1/4+x)/(1/2)= ?
(1/3+1/5-1/7)/(1/x)= ?
(a/b+2+b/a)/(a/b-b/a)= ?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The key is to multiply the numerator and denominator of the "big" fraction by the Lowest Common Denoinator (LCD) of the "small" fractions in that "big" fraction.

%28a%2Fb%2Bc%29%2F%28a%2Fb-c%29
The LCD of the "small" fractions is b
%28%28a%2Fb%2Bc%29%2F%28a%2Fb-c%29%29%2A%28b%2Fb%29+=+%28a+%2B+bc%29%2F%28a+-+bc%29

%281%2F4%2Bx%29%2F%281%2F2%29
The LCD is 4
%28%281%2F4%2Bx%29%2F%281%2F2%29%29%2A%284%2F4%29+=+%281+%2B+4x%29%2F2+=+1%2F2+%2B+2x
Since the denominator is just a single term we might also change the "divide by 1/2" to "multiply by the reciprocal of 1/2". The reciprocal of 1/2 is 2/1 = 2.:
%281%2F4%2Bx%29%2F%281%2F2%29+=+%281%2F4%2Bx%29%2A2+=+1%2F2+%2B+2x

%281%2F3%2B1%2F5-1%2F7%29%2F%281%2Fx%29
The LCD is 105x

Since the denominator is just a single term we might also change the "divide by 1/x" to "multiply by the reciprocal of 1/x". The reciprocal of 1/x is x/1 = x.:
. If you then get the denominators the same and add and subtract you get the answer above: 41x/105

%28a%2Fb%2B2%2Bb%2Fa%29%2F%28a%2Fb-b%2Fa%29
The LCD is ab

While none of the previous answers would reduce, this one will. We reduce by factoring and canceling common factors:

One of the (a+b)'s in the numerator cancels with the one in the denominator leaving:
%28a+%2B+b%29%2F%28a+-+b%29