Question

What is the sum of the rational expressions below?
3x-1/2x + 3x/x-1

Answer 1

`(9x^2-4x+1)/(2x(x-1))`

Explanation:

The given expression is:

`(3x-1)/(2x)+(3x)/(x-1)`

Simplifying the above expression, we get

`((3x-1)(x-1)+3x(2x))/(2x(x-1))`

`(3x^2-x-3x+1+6x^2)/(2x(x-1))`

`(9x^2-4x+1)/(2x(x-1))`

which is the required sum of the given rational expression.

Answer 2

In order to find the sum of the given rational expressions above, here are the steps.
Firstly, you need to find the LCM of the least common denominator.
So it would look like this:
3x-1 + 3x (3x-1)(x-1) + (2x)(3x)
------ ------- = ---------------------------
2x x-1 2x(x-1)

3x^2-4x+1+6x^2
----------------------
2x(x-1)
And the final result would be this:
9x^2-4x+1
--------------
2x(x-1)

9x^2-4x+1
--------------
2x^2-2x

Hope that this is the answer that you are looking for.