Year 12s: what will be the first way you research your future options? >>

Don't know where I've gone wrong - Algebra

The question asked me to solve:
((x+2)/3x ) + ((x-2)/2x) =3
Since it was a fraction, I cross multiplied the bases so they looked like:
2x( x+2) + 3x(x-2) =3 2x^2 +4x +3x^2 - 6x.=3
I then simplified : 5x^2 -2x =3
This is where I'm a little-lost I. I think I have to factorise as to get: x (5x-2) = 3, so that the answer would look like x = 3/5x-2, but that wouldn't give me a value for x.
Please help

Reply 1

ghostwalker

Original post by Botcampers

The question asked me to solve:
((x+2)/3x ) + ((x-2)/2x) =3
Since it was a fraction, I cross multiplied the bases so they looked like:
2x( x+2) + 3x(x-2) =3 2x^2 +4x +3x^2 - 6x.=3

You say you "cross multiplied". That's a technique used when you have two fractions that are equal, and there the multiplication goes across he equals sign, so to speak.

That's not the case here.

You're adding two fractions. The only way to do that is to put them over a common denominator.

One denominator is "3x" and the other is "2x". What might a common denominator be? One that they both divide into.

Reply 2

Squish•

If you cross multiply u have to multiply the bottom numbers by the number 3 too

Reply 3

-oof-

Original post by Botcampers

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

1- You want to get a common denominator so you multiply the first fraction by 2 and the second fraction by 3:

(2(x+2)/2(3x)) + (3(x-2)/3(2x)) = (2x+4/6x) + (3x-6/6x)

2- Put both fractions into one:

2x+4+3x-6/6x = 3

3- Multiply both sides by 6x to get rid of the denominator on the left:

2x+4+3x-6 = 18x

4- Solve the equation:

5x-2 = 18x
-2 = 13x
13x = -2
x = -2/13

(edited 7 years ago)