Question 12283
I don't know what you did to get your answer, but I didn't get that.


First, this is an equation, and there are several ways to solve it.  I think the easiest way to solve it, since it is equal to zero, add the second fraction {{{4/(x-1) }}} to both sides and write this as a fraction equal to the negative of a fraction.  As I said, this is NOT the only way, but I think it will be the easiest to explain and easiest to understand:

{{{(2x+3)/x + 4/(x-1) - 4/(x-1) =0- 4/(x-1) }}}
{{{ (2x+3)/x = -4/(x-1) }}}


Remember {{{a/b= c/d}}} means that {{{a*d = b*c}}}


So,

{{{ (2x+3)/x = -4/(x-1) }}} means that {{{(2x+3)*(x-1)= -4*x }}}


Multiplying it out:
{{{2x^2+x-3 = -4x}}}


Set equal to zero by adding +4x to each side:

{{{2x^2 +x - 3 + 4x = -4x + 4x}}}
{{{2x^2 + 5x - 3 = 0}}}


As CHANCE would have it (yeah, right!) THE TRINOMIAL FACTORS!!
{{{ (2x + 1)*(x-3) = 0}}}


First solution:
{{{2x+1 =0}}}
{{{2x = -1 }}}
{{{x= 1/2}}}


Second solution:
{{{x- 3= 0}}}
{{{x= 3}}}


R^2 at SCC