Question 282913
{{{(3x-5)/(x+2)=(x-1)/(2x-1)}}} Start with the given equation.



{{{(3x-5)(2x-1)=(x+2)(x-1)}}} Cross multiply



{{{6x^2-13x+5=x^2+x-2}}} FOIL



{{{6x^2-13x+5-x^2-x+2=0}}} Get every term to the left side.



{{{5x^2-14x+7=0}}} Combine like terms.



Notice that the quadratic {{{5x^2-14x+7}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=5}}}, {{{B=-14}}}, and {{{C=7}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-14) +- sqrt( (-14)^2-4(5)(7) ))/(2(5))}}} Plug in  {{{A=5}}}, {{{B=-14}}}, and {{{C=7}}}



{{{x = (14 +- sqrt( (-14)^2-4(5)(7) ))/(2(5))}}} Negate {{{-14}}} to get {{{14}}}. 



{{{x = (14 +- sqrt( 196-4(5)(7) ))/(2(5))}}} Square {{{-14}}} to get {{{196}}}. 



{{{x = (14 +- sqrt( 196-140 ))/(2(5))}}} Multiply {{{4(5)(7)}}} to get {{{140}}}



{{{x = (14 +- sqrt( 56 ))/(2(5))}}} Subtract {{{140}}} from {{{196}}} to get {{{56}}}



{{{x = (14 +- sqrt( 56 ))/(10)}}} Multiply {{{2}}} and {{{5}}} to get {{{10}}}. 



{{{x = (14 +- 2*sqrt(14))/(10)}}} Simplify the square root  



{{{x = (14+2*sqrt(14))/(10)}}} or {{{x = (14-2*sqrt(14))/(10)}}} Break up the expression.  



{{{x = (7+sqrt(14))/(5)}}} or {{{x = (7-sqrt(14))/(5)}}} Reduce.  



So the solutions are {{{x = (7+sqrt(14))/(5)}}} or {{{x = (7-sqrt(14))/(5)}}}



So it looks like you're on the right track.