Simplifying complex fraction help?

Question

Simplifying complex fraction help?
Simplifying complex fraction help?
( 1 / 2x - 3) - ( 1 / 2x + 3) ALL OVER ( 1 / 2x ) - ( 1 / 2x + 3)

Please help me with simplifying this complex fraction! I am getting super confused and need a description on how to get through the problem, thank you!
I know the answer is 4x / 2x -3, which is correct. I just need to know how to do it!

Answer 1

Okay so first of all you need to find the one common denominator for all the fractions in the expression. One you find that fraction, you multiply both the complex numerator and complex denominator by this expression. The easiest way to find this common denominator is to multiply all the different denominators together. So your denominators are (2x) and (2x-3) and (2x+3). So your common denominator for your complex fraction would be (2x)(2x-3)(2x+3).



[2x][2x-3][2x+3]{( 1 / 2x - 3) - ( 1 / 2x + 3)} ALL OVER [2x][2x-3][2x+3]{( 1 / 2x ) - ( 1 / 2x + 3)}



As you should know, we multiply only the numerator which in this case are all 1's. After similar numerators and denominators cancel out, you should be left with:

[(2x)(2x+3)] - [(2x)(2x-3)]

-------------------------------------- simplify ....[ there's a (-) sign so you cant cancel ]

[(2x-3)(2x+3)] - [(2x)(2x-3)]





(4x^2+6x) - (4x^2-6x)

--------------------------------- simplify and distribute your negative sign

(4x^2+6x-6x-9) - (4x^2-6x)





12x/6x-9 --> take 3 as a common factor, you get 3(4x)/3(2x-3) --> the 3's cancel and you get 4x/2x-3.

Answer 2

it's a bit complicated so i'm going to try my best to explain it to you

let's start with the first part:

(1/2x-3)-(1/2x+3) : you need to have the same denominator, so you multiply the first one by (2x+3)/(2x+3) and the second one by (2x-3)/(2x-3). you get:

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

now for the second part, you do the exact same thing so get the same denominator and you get:

(2x+3-2x)/(2x)(2x+3) = 3/(2x)(2x+3)



then you divide the 1st one by the 2nd:

6/(2x-3)(2x+3) ALL OVER 3/(2x)(2x+3) =

[6/(2x-3)(2x+3)] X [(2x)(2x+3)/3] =

[ 6 X 2x X (2x+3) ] / [3 X (2x-3)(2x+3)] =

(2 X 2x) / (2x-3) =

4x / (2x-3)



it's easier to copy it down on a piece of paper before trying to understand it

Answer 3

it must be complicated, yet its no longer complicated. .. (3 / 4y) - (2 / y) / (one million / y) + (3 / 2y) = (3 / 4y) - (2 / y) * (y / one million) + (3 / 2y) = (3 / 4y) - (2 / one million) + (3 *2 / 4y) = (3 / 4y) - 2 + (6 / 4y) = (3 + 6) / (4y) - 2 = 9 / (4y) - 2 = 9 / (4y) - 8y/(4y) = ( 9 - 8y ) /(4y)