Question 203062
{{{((k^2+3k-10)/36)(3/(k^2-4))}}} Start with the given expression.



{{{(((k+5)(k-2))/36)(3/(k^2-4))}}} Factor the first numerator



{{{(((k+5)(k-2))/(12*3))(3/(k^2-4))}}} Factor the first denominator



{{{(((k+5)(k-2))/(12*3))(3/((k-2)(k+2)))}}} Factor the second denominator (hint: use the difference of squares formula)



{{{(3(k+5)(k-2))/(12*3(k-2)(k+2))}}} Combine the fractions.



{{{(highlight(3)(k+5)highlight((k-2)))/(12*highlight(3)highlight((k-2))(k+2))}}} Highlight the common terms.



{{{(cross(3)(k+5)cross((k-2)))/(12*cross(3)cross((k-2))(k+2))}}} Cancel out the common terms.



{{{(k+5)/(12(k+2))}}} Simplify



{{{(k+5)/(12k+24)}}} Distribute




So {{{((k^2+3k-10)/36)(3/(k^2-4))}}} simplifies to {{{(k+5)/(12k+24)}}}



In other words, {{{((k^2+3k-10)/36)(3/(k^2-4))=(k+5)/(12k+24)}}}