Question 97392
{{{(5a-12)/(a^2-8a+15) - (3a - 2)/(a^2 - 8a + 15)}}} Start with the given expression


{{{(5a-12- (3a - 2))/(a^2-8a+15) }}} Combine the fractions



{{{(5a-12- 3a + 2)/(a^2-8a+15) }}} Distribute the negative



{{{(2a-10)/(a^2-8a+15) }}} Combine like terms



{{{2(a-5)/(a^2-8a+15) }}} Factor out the GCF



{{{2(a-5)/((a-5)(a-3)) }}} Factor the denominator



{{{2*cross((a-5))/(cross((a-5))(a-3)) }}} Cancel like terms



{{{2/(a-3) }}} Simplify




Check:



To verify the answer, simply compare the graphs of {{{(5a-12)/(a^2-8a+15) - (3a - 2)/(a^2 - 8a + 15)}}} and {{{2/(a-3) }}}. If they are equivalent (they are), then the answer is verified.