Question 413652
{{{5/(x^2+x-6)}}} = 2 + {{{(x-3)/(x-2)}}} 
Factor the 1st denominator
{{{5/((x+3)(x-2))}}} = 2 + {{{(x-3)/(x-2)}}}
the common denominator consists of the factors of both denominators
the common denominator is (x+3)(x-2)*
Multiply each term by the common denominator
(x+3)(x-2)*{{{5/((x+3)(x-2))}}} = (x+3)(x-2)*2 + (x+3)(x-2)*{{{(x-3)/(x-2)}}}
Cancel out the denominators that you can and you have:
5 = 2(x+3)(x-2) + (x+3)(x-3)
FOIL
5 = 2(x^2 - 2x + 3x - 6) + (x^2 -3x + 3x - 9)
5 = 2(x^2 + x - 6) + (x^2-9)
5 = 2x^2 + 2x - 12 + x^2 - 9
Combine like terms
0 = 2x^2 + x^2 + 2x - 12 - 9 - 5
a quadratic equation
3x^2 + 2x - 26 = 0
You have to solve this equation using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
In this equation; a=3; b=2; c=-26
{{{x = (-2 +- sqrt(2^2-4*3*-26 ))/(2*3) }}}
{{{x = (-2 +- sqrt(4-(-312) ))/(6) }}}
{{{x = (-2 +- sqrt(4 + 312 ))/(6) }}}
{{{x = (-2 +- sqrt(316 ))/(6) }}}
Two solutions
{{{x = (-2 + 17.776)/(6) }}}
x = {{{15.776/6}}}
x = 2.63
and
{{{x = (-2 - 17.776)/(6) }}}
x = {{{19.776/6}}}
x = -3.296
:
You job is to check both these solutions in the original equation