Solving equations with fractions: 2x/(x+6) + 1/(x-1) = 2

[Mwnciboy]

Hi, I've been struggling with solving the following equation:
2x/(x+6) + 1/(x-1) = 2

I've tried multiplying by (x+6)(x-1) but it all gets confusing and complicated.
I don't want the answer, just some advice on where to begin, thanks.

 

[Deleted member 4993]

Hi, I've been struggling with solving the following equation:
2x/(x+6) + 1/(x-1) = 2

I've tried multiplying by (x+6)(x-1) but it all gets confusing and complicated.
I don't want the answer, just some advice on where to begin, thanks.

From your attempt I am assuming the actual equation is:

2x/(x+6) + 1/(x-1) = 2..................... those parentheses are super important to make your problem decipherable

assuming x \(\displaystyle \ne -6\) and x \(\displaystyle \ne 1\), we get,

2x(x-1) + (x+6) = 2(x+6)(x-1)

2x^2 - 2x + x + 6 = 2 * [x^2 + 5x -6]

2x^2 - 2x + x + 6 = 2 x^2 + 10x - 12

Now move everything to the left-hand-side of the "=", collect terms with same powers of 'x', and continue....

If you are still stuck - please reply showing your steps, to get further help.

 

[Mwnciboy]

From your attempt I am assuming the actual equation is:

2x/(x+6) + 1/(x-1) = 2..................... those parentheses are super important to make your problem decipherable

assuming x \(\displaystyle \ne -6\) and x \(\displaystyle \ne 1\), we get,

2x(x-1) + (x+6) = 2(x+6)(x-1)

2x^2 - 2x + x + 6 = 2 * [x^2 + 5x -6]

2x^2 - 2x + x + 6 = 2 x^2 + 10x - 12

Now move everything to the left-hand-side of the "=", collect terms with same powers of 'x', and continue....

If you are still stuck - please reply showing your steps, to get further help.

Hi, thanks for your help, I've got it now. Sorry if original equation wasn't clear.