Question 200968


{{{((5x^4+2x^3)/(2x^4+3x^3))((2x^3+x^2-3x)/(5x^2-3x-2))}}} Start with the given expression.



{{{((x^3(5x+2))/(2x^4+3x^3))((2x^3+x^2-3x)/(5x^2-3x-2))}}} Factor {{{5x^4+2x^3}}} to get {{{x^3(5x+2)}}}.



{{{((x^3(5x+2))/(x^3(2x+3)))((2x^3+x^2-3x)/(5x^2-3x-2))}}} Factor {{{2x^4+3x^3}}} to get {{{x^3(2x+3)}}}.



{{{((x^3(5x+2))/(x^3(2x+3)))((x(2x+3)(x-1))/(5x^2-3x-2))}}} Factor {{{2x^3+x^2-3x}}} to get {{{x(2x+3)(x-1)}}}.



{{{((x^3(5x+2))/(x^3(2x+3)))((x(2x+3)(x-1))/((5x+2)(x-1)))}}} Factor {{{5x^2-3x-2}}} to get {{{(5x+2)(x-1)}}}.



{{{(x*x^3(5x+2)(2x+3)(x-1))/(x^3(2x+3)(5x+2)(x-1))}}} Combine the fractions. 



{{{(x*highlight(x^3)*highlight((5x+2))highlight((2x+3))highlight((x-1)))/(highlight(x^3)highlight((2x+3))highlight((5x+2))highlight((x-1)))}}} Highlight the common terms. 



{{{(x*cross(x^3)*cross((5x+2))cross((2x+3))cross((x-1)))/(cross(x^3)cross((2x+3))cross((5x+2))cross((x-1)))}}} Cancel out the common terms. 



{{{x}}} Simplify. 



So {{{((5x^4+2x^3)/(2x^4+3x^3))((2x^3+x^2-3x)/(5x^2-3x-2))}}} simplifies to {{{x}}}.



In other words, {{{((5x^4+2x^3)/(2x^4+3x^3))((2x^3+x^2-3x)/(5x^2-3x-2))=x}}}