Question 133665
{{{(2*x^3+2*x^2-4*x)/(x^3+2x^2-3x)}}} Start with the given expression



{{{(2x(x+2)(x-1))/(x^3+2x^2-3x)}}} Factor out an "x" from {{{2*x^3+2*x^2-4*x}}} to get {{{x(2*x^2+2*x-4)}}}. Now factor the inner expression {{{2*x^2+2*x-4}}} to get {{{(x+2)(x-1)}}}
                     



{{{(2x(x+2)(x-1))/(x(x+3)(x-1))}}} Factor out an "x" from {{{x^3+2x^2-3x}}} to get {{{x(x^2+2x-3)}}}. Now factor the inner expression {{{2*x^2+2*x-4}}} to get {{{(x+3)(x-1)}}}        



{{{(2cross(x)(x+2)cross((x-1)))/(cross(x)(x+3)cross((x-1)))}}} Cancel like terms



{{{(2(x+2))/(x+3)}}} Simplify




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Answer:


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