Question 42112
{{{(5a-12)/(a^2-8a+ 5)}}}

= {{{(5a - 12)/(a^2 - 3a -5a + 15)}}}
= {{{(5a - 12)/(a(a - 3) -5(a- 3))}}}
= {{{(5a- 12)/((a - 3)(a -5))}}}


Similarly,
{{{(3a - 2)/(a^2 - 8a + 15)}}}
= {{{(3a - 2)/((a - 3)(a -5))}}}


Then, {{{(5a -12)/(a^2 - 8a + 15) - (3a - 2)/(a^2 - 8a + 15)}}}
= {{{(5a -12)/((a -3)(a - 5)) - (3a - 2)/((a - 3)(a - 5))}}}
= {{{((5a-12)-(3a-2))/((a-3)(a-5))}}}
= {{{(5a-12-3a+2)/((a-3)(a-5))}}}
= {{{(2a-10)/((a-3)(a-5))}}}
= {{{(2(a-5))/((a-3)(a-5))}}}
= {{{2/(a-3)}}}