Question 92159
Find the solution sets for the following:
Assume you mean:
{{{2/((x+1))}}} + 6 = {{{3/((x-1))}}}
:
Multiply each term in the equation by (x+1)(x-1), results in:
2(x-1) + 6(x+1)(x-1) = 3(x+1)
:
2x - 2 + 6(x^2 - 1) = 3x + 3; FOILed (x+1)*(x-1)
2x - 2 + 6x^2 - 6 = 3x + 3
:
Arrange as a quadratic equation on the left:
6x^2 + 2x - 3x - 2 - 6 - 3 = 0
:
6x^2 - x - 11 = 0
:
Use the quadratic formula to find x: a=6; b=-1; c=-11
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{x = (-(-1) +- sqrt(-1^2 - 4 * 6 * -11 ))/(2*6) }}}
:
{{{x = (+1 +- sqrt(+1 - (-264) ))/(12) }}}; minus a minus is a plus
:
{{{x = (+1 +- sqrt( 265 ))/(12) }}}
:
Two solutions:
{{{x = (+1 + 16.2788)/(12) }}}
x = {{{+17.2788/12}}}
x = +1.44
and
{{{x = (+1 - 16.2788)/(12) }}}
x = {{{-15.2788/12}}}
x = -1.273
:
You should check these solutions in the original equation.