Question 195667
{{{(5-x)/(2-x)-(3-2x)/(2x)=1}}} Start with the given equation.



{{{2x*cross((x-2))((5-x)/cross((x-2)))-cross(2x)(2-x)((3-2x)/cross(2x))=2x(2-x)(1)}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{2x(2-x)}}}. Doing this will eliminate all of the fractions.



{{{2x(5-x)-(2-x)(3-2x)=2x(2-x)(1)}}} Cancel out and simplify



{{{2x(5-x)-(2-x)(3-2x)=2x(2-x)}}} Multiply



{{{2x(5-x)-(6-7x+2x^2)=2x(2-x)}}} FOIL



{{{10x-2x^2-6+7x-2x^2=4x-2x^2}}} Distribute



{{{10x-2x^2-6+7x-2x^2-4x+2x^2=0}}} Get all terms to the left side.



{{{-2x^2+13x-6=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=-2}}}, {{{b=13}}}, and {{{c=-6}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(13) +- sqrt( (13)^2-4(-2)(-6) ))/(2(-2))}}} Plug in  {{{a=-2}}}, {{{b=13}}}, and {{{c=-6}}}



{{{x = (-13 +- sqrt( 169-4(-2)(-6) ))/(2(-2))}}} Square {{{13}}} to get {{{169}}}. 



{{{x = (-13 +- sqrt( 169-48 ))/(2(-2))}}} Multiply {{{4(-2)(-6)}}} to get {{{48}}}



{{{x = (-13 +- sqrt( 121 ))/(2(-2))}}} Subtract {{{48}}} from {{{169}}} to get {{{121}}}



{{{x = (-13 +- sqrt( 121 ))/(-4)}}} Multiply {{{2}}} and {{{-2}}} to get {{{-4}}}. 



{{{x = (-13 +- 11)/(-4)}}} Take the square root of {{{121}}} to get {{{11}}}. 



{{{x = (-13 + 11)/(-4)}}} or {{{x = (-13 - 11)/(-4)}}} Break up the expression. 



{{{x = (-2)/(-4)}}} or {{{x =  (-24)/(-4)}}} Combine like terms. 



{{{x = 1/2}}} or {{{x = 6}}} Simplify. 



So the answers are {{{x = 1/2}}} or {{{x = 6}}}