# Math Help - to solve the equation

1. ## to solve the equation

Please help to solve the following equation. At the end of the calculation, I dont know how to factorise the equation. Please help me with simple steps
(x+1/x-2 + 3x) - (1/x+1) = 6

With Many Thanks
Alan Paul

2. ## Re: to solve the equation

Originally Posted by alanpaul
Please help to solve the following equation. At the end of the calculation, I dont know how to factorise the equation. Please help me with simple steps
(x+1/x-2 + 3x) - (1/x+1) = 6

With Many Thanks
Alan Paul
$\dfrac{x+1}{x-2}+\dfrac{3x-1}{x+1}=6$

$\dfrac{(x+1)^2+(3x-1)(x-2)}{(x-2)(x+1)}=6$

$\dfrac{x^2+2x+1+3x^2-7x+2}{(x-2)(x+1)}=6$

$\dfrac{4x^2-5x+3}{x^2-x-2}=6$

$4x^2-5x+3=6(x^2-x-2)=6x^2-6x-12$

$2x^2-x-15=0$

$(x-3)(2x+5)=0$

$x=3$ OR $x=-\dfrac 5 2$