Question 195563


{{{(-3x)/(x+1)=(-2)/(x-1)}}} Start with the given equation.



{{{cross((x+1))(x-1)((-3x)/cross((x+1)))=(x+1)cross((x-1))((-2)/cross((x-1)))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{(x+1)(x-1)}}}. Doing this will eliminate all of the fractions.



{{{-3x(x-1)=-2(x+1)}}} Multiply and simplify



{{{-3x^2+3x=-2x-2}}} Distribute



{{{-3x^2+3x+2x+2=0}}} Get everything to the left side



{{{-3x^2+5x+2=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=-3}}}, {{{b=5}}}, and {{{c=2}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(5) +- sqrt( (5)^2-4(-3)(2) ))/(2(-3))}}} Plug in  {{{a=-3}}}, {{{b=5}}}, and {{{c=2}}}



{{{x = (-5 +- sqrt( 25-4(-3)(2) ))/(2(-3))}}} Square {{{5}}} to get {{{25}}}. 



{{{x = (-5 +- sqrt( 25--24 ))/(2(-3))}}} Multiply {{{4(-3)(2)}}} to get {{{-24}}}



{{{x = (-5 +- sqrt( 25+24 ))/(2(-3))}}} Rewrite {{{sqrt(25--24)}}} as {{{sqrt(25+24)}}}



{{{x = (-5 +- sqrt( 49 ))/(2(-3))}}} Add {{{25}}} to {{{24}}} to get {{{49}}}



{{{x = (-5 +- sqrt( 49 ))/(-6)}}} Multiply {{{2}}} and {{{-3}}} to get {{{-6}}}. 



{{{x = (-5 +- 7)/(-6)}}} Take the square root of {{{49}}} to get {{{7}}}. 



{{{x = (-5 + 7)/(-6)}}} or {{{x = (-5 - 7)/(-6)}}} Break up the expression. 



{{{x = (2)/(-6)}}} or {{{x =  (-12)/(-6)}}} Combine like terms. 



{{{x = -1/3}}} or {{{x = 2}}} Simplify. 



So the answers are {{{x = -1/3}}} or {{{x = 2}}}