Question 200969


{{{((5x^2-125)/(x^3+5x^2))((6x^2+2x)/(5x-25))}}} Start with the given expression.



{{{((5(x-5)(x+5))/(x^3+5x^2))((6x^2+2x)/(5x-25))}}} Factor {{{5x^2-125}}} to get {{{5(x-5)(x+5)}}}.



{{{((5(x-5)(x+5))/(x*x(x+5)))((6x^2+2x)/(5x-25))}}} Factor {{{x^3+5x^2}}} to get {{{x*x(x+5)}}}.



{{{((5(x-5)(x+5))/(x*x(x+5)))((2x(3x+1))/(5x-25))}}} Factor {{{6x^2+2x}}} to get {{{2x(3x+1)}}}.



{{{((5(x-5)(x+5))/(x*x(x+5)))((2x(3x+1))/(5(x-5)))}}} Factor {{{5x-25}}} to get {{{5(x-5)}}}.



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



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



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



{{{(2(3x+1))/x}}} Simplify. 



{{{(6x+2)/x}}} Distribute



So {{{((5x^2-125)/(x^3+5x^2))((6x^2+2x)/(5x-25))}}} simplifies to {{{(6x+2)/x}}}.



In other words, {{{((5x^2-125)/(x^3+5x^2))((6x^2+2x)/(5x-25))=(6x+2)/x}}}