Question 167696
{{{(x+1)/(1+x)-(1)/(3-x)=(6)/(35)}}} Start with the given equation.



{{{35cross((1+x))(3-x)((x+1)/cross((1+x)))-35(1+x)cross((3-x))((1)/cross((3-x)))=cross(35)(1+x)(3-x)((6)/cross(35))}}} Multiply <font size="4"><b>EVERY</b></font> term on both sides by the LCD {{{35(1+x)(3-x)}}}. Doing this will eliminate all of the fractions.



{{{35(3-x)(x+1)-35(1+x)=6(1+x)(3-x)}}} Multiply and simplify



{{{35(3+2x-x^2)-35(1+x)=6(3+2x-x^2)}}} FOIL



{{{105+70x-35x^2-35-35x=18+12x-6x^2}}} Distribute



{{{-35x^2+35x+70=-6x^2+12x+18}}} Combine like terms.



{{{-35x^2+35x+70+6x^2-12x-18=0}}} Get all terms to the left side.



{{{-29x^2+23x+52=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=-29}}}, {{{b=23}}}, and {{{c=52}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(23) +- sqrt( (23)^2-4(-29)(52) ))/(2(-29))}}} Plug in  {{{a=-29}}}, {{{b=23}}}, and {{{c=52}}}



{{{x = (-23 +- sqrt( 529-4(-29)(52) ))/(2(-29))}}} Square {{{23}}} to get {{{529}}}. 



{{{x = (-23 +- sqrt( 529--6032 ))/(2(-29))}}} Multiply {{{4(-29)(52)}}} to get {{{-6032}}}



{{{x = (-23 +- sqrt( 529+6032 ))/(2(-29))}}} Rewrite {{{sqrt(529--6032)}}} as {{{sqrt(529+6032)}}}



{{{x = (-23 +- sqrt( 6561 ))/(2(-29))}}} Add {{{529}}} to {{{6032}}} to get {{{6561}}}



{{{x = (-23 +- sqrt( 6561 ))/(-58)}}} Multiply {{{2}}} and {{{-29}}} to get {{{-58}}}. 



{{{x = (-23 +- 81)/(-58)}}} Take the square root of {{{6561}}} to get {{{81}}}. 



{{{x = (-23 + 81)/(-58)}}} or {{{x = (-23 - 81)/(-58)}}} Break up the expression. 



{{{x = (58)/(-58)}}} or {{{x =  (-104)/(-58)}}} Combine like terms. 



{{{x = -1}}} or {{{x = 52/29}}} Simplify. 



So the possible answers are {{{x = -1}}} or {{{x = 52/29}}} 

  

However, if you plug in {{{x = -1}}}, then you will get a division by zero. So the only answer is {{{x = 52/29}}} 




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Answer:



So the solution is {{{x = 52/29}}} which approximates to {{{x=1.793}}}