factorisation of a quadratic equation that is a fraction :/

Hey guys im stuck on an equation and just cant seem to get the right answer. I know there must be something wrong with my working. Could someone please show me how you multiply out the denominator to solve this equation.

** 1+ 6/x-1 = 1/x+1**

Thank you in advance for any help.

Re: factorisation of a quadratic equation that is a fraction :/

Hi , multiply equation by

Re: factorisation of a quadratic equation that is a fraction :/

Quote:

Originally Posted by

**princeps** Hi , multiply equation by

Thank you for your quick reply. I tried that and still cant seem to get the correct answer. I know the answer because I have checked and I cant even work backwards to get it. Ill show my working out and maybe someone will know where im going wrong..

1+ 6/x-1 = 1/x+1

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

1+6x+6-x-1 = 0

5x+6 = 0

)

(

)

But the proper answer is= X^{2}+5x+6=0

x=-3 & -2

I cant seem to find where x^{2} came from.

Re: factorisation of a quadratic equation that is a fraction :/

You have to multiply by also .

Re: factorisation of a quadratic equation that is a fraction :/

In such cases go by the following algorithm.

Step-1: Multiply the equation be the LCM of the denominator which in this case is (x-1)(x=1)

.(x-1)(x+1)[ 1 + 6/(x-1) = 1/(x+1) OR x^2 -1 + 6(x+1) = (x-1)

Step 2: Simplify the equation

x^2 -1 + 6x+6 = x-1

x^2 -1 + 6x+6 -x+1= 0

x^2 + 5x+6 = 0

(x+3)(x+2) = 0

etc.

Re: factorisation of a quadratic equation that is a fraction :/

Ahhh I think I get it now! Thanks heaps for all the help.

Re: factorisation of a quadratic equation that is a fraction :/

Quote:

Originally Posted by

**jewelmaule** Hey guys im stuck on an equation and just cant seem to get the right answer. I know there must be something wrong with my working. Could someone please show me how you multiply out the denominator to solve this equation.

** 1+ 6/x-1 = 1/x+1**

Thank you in advance for any help.

I assume that your equation is . Some brackets where they're needed would be nice... Anyway...

Re: factorisation of a quadratic equation that is a fraction :/

Quote:

Originally Posted by

**Prove It** I assume that your equation is

. Some brackets where they're needed would be nice... Anyway...

Thank you for your help. Yeah I have been trying to figure out how everyone gets their equations in that format on this forum.