Question 173382


{{{(x-4)/(x+1)+(4)/(x)=(29)/(30)}}} Start with the given equation.



{{{30x*cross((x+1))((x-4)/cross((x+1)))+30cross(x)(x+1)((4)/cross(x))=cross(30)x(x+1)((29)/cross(30))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{30x(x+1)}}}. Doing this will eliminate all of the fractions.



{{{30x(x-4)+30*4(x+1)=29x(x+1)}}} Simplify.



{{{30x(x-4)+120(x+1)=29x(x+1)}}} Multiply.



{{{30x^2-120x+120x+120=29x^2+29x}}} Distribute.



{{{30x^2-120x+120x+120=29x^2+29x}}} Start with the given equation.



{{{30x^2-120x+120x+120-29x^2-29x=0}}} Subtract {{{29x^2}}} from both sides. Subtract 29x from both sides.



{{{x^2-29x+120=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-29}}}, and {{{c=120}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-29) +- sqrt( (-29)^2-4(1)(120) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-29}}}, and {{{c=120}}}



{{{x = (29 +- sqrt( (-29)^2-4(1)(120) ))/(2(1))}}} Negate {{{-29}}} to get {{{29}}}. 



{{{x = (29 +- sqrt( 841-4(1)(120) ))/(2(1))}}} Square {{{-29}}} to get {{{841}}}. 



{{{x = (29 +- sqrt( 841-480 ))/(2(1))}}} Multiply {{{4(1)(120)}}} to get {{{480}}}



{{{x = (29 +- sqrt( 361 ))/(2(1))}}} Subtract {{{480}}} from {{{841}}} to get {{{361}}}



{{{x = (29 +- sqrt( 361 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (29 +- 19)/(2)}}} Take the square root of {{{361}}} to get {{{19}}}. 



{{{x = (29 + 19)/(2)}}} or {{{x = (29 - 19)/(2)}}} Break up the expression. 



{{{x = (48)/(2)}}} or {{{x =  (10)/(2)}}} Combine like terms. 



{{{x = 24}}} or {{{x = 5}}} Simplify. 



So the answers are {{{x = 24}}} or {{{x = 5}}}