Question 266169
{{{((a+b)/(2))((10x+2)/(b^2-a^2))}}} Start with the given expression.



{{{((a+b)/(2))((2(5x+1))/(b^2-a^2))}}} Factor {{{10x+2}}} to get {{{2(5x+1)}}}.



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



{{{(2(a+b)(5x+1))/(2(b+a)(b-a))}}} Combine the fractions. 



{{{(2(a+b)(5x+1))/(2(a+b)(b-a))}}} Rewrite {{{b+a}}} (in the denominator) as {{{a+b}}}



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



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



{{{(5x+1)/(b-a)}}} Simplify. 



So {{{((a+b)/(2))((10x+2)/(b^2-a^2))}}} simplifies to {{{(5x+1)/(b-a)}}}.



In other words, {{{((a+b)/(2))((10x+2)/(b^2-a^2))=(5x+1)/(b-a)}}}