Question 177043
{{{5/(x+1) + 4/3 =(x+1)/(x-1)}}} Start with the given equation.



{{{5(3(x-1)) + 4((x+1)(x-1)) =3(x+1)(x+1)}}} Multiply EVERY term by the LCD {{{3(x+1)(x-1)}}} to clear the fractions.



{{{15(x-1) + 4((x+1)(x-1)) =3(x+1)(x+1)}}} Multiply



{{{15(x-1) + 4(x^2-1) =3(x^2+2x+1)}}} FOIL



{{{15x-15 + 4x^2-4 =3x^2+6x+3}}} Distribute



{{{15x-19 + 4x^2 =3x^2+6x+3}}} Combine like terms.



{{{15x-19+4x^2-3x^2-6x-3=0}}} Get all terms to the left side.



{{{x^2+9x-22=0}}} Combine like terms.



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Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=9}}}, and {{{c=-22}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(9) +- sqrt( (9)^2-4(1)(-22) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=9}}}, and {{{c=-22}}}



{{{x = (-9 +- sqrt( 81-4(1)(-22) ))/(2(1))}}} Square {{{9}}} to get {{{81}}}. 



{{{x = (-9 +- sqrt( 81--88 ))/(2(1))}}} Multiply {{{4(1)(-22)}}} to get {{{-88}}}



{{{x = (-9 +- sqrt( 81+88 ))/(2(1))}}} Rewrite {{{sqrt(81--88)}}} as {{{sqrt(81+88)}}}



{{{x = (-9 +- sqrt( 169 ))/(2(1))}}} Add {{{81}}} to {{{88}}} to get {{{169}}}



{{{x = (-9 +- sqrt( 169 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-9 +- 13)/(2)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (-9 + 13)/(2)}}} or {{{x = (-9 - 13)/(2)}}} Break up the expression. 



{{{x = (4)/(2)}}} or {{{x =  (-22)/(2)}}} Combine like terms. 



{{{x = 2}}} or {{{x = -11}}} Simplify. 



So the answers are {{{x = 2}}} or {{{x = -11}}}