Question 189074


{{{((x^2-25)/(9))((x+5)/(x-5))}}} Start with the given expression.



{{{(((x-5)(x+5))/(9))((x+5)/(x-5))}}} Factor {{{x^2-25}}} to get {{{(x-5)(x+5)}}} (use the difference of squares).



{{{((x-5)(x+5)(x+5))/(9(x-5))}}} Combine the fractions. 



{{{(highlight((x-5))(x+5)(x+5))/(9*highlight((x-5)))}}} Highlight the common terms. 



{{{(cross((x-5))(x+5)(x+5))/(9*cross((x-5)))}}} Cancel out the common terms. 



{{{((x+5)(x+5))/(9)}}} Simplify. 



{{{(x^2+10x+25)/(9)}}} FOIL



So {{{((x^2-25)/(9))((x+5)/(x-5))}}} simplifies to {{{(x^2+10x+25)/(9)}}}.



In other words, {{{((x^2-25)/(9))((x+5)/(x-5))=(x^2+10x+25)/(9)}}} where {{{x<>5}}}