Question 1126092
{{{(a-4)/(a^2+5a) -2/(a+5)=1/(a^3+7a^2+10a )}}}


{{{(a-4)/a(a+5) -2/(a+5)=1/a(a^2+7a+10 )}}}


{{{(a-4)/a(a+5) -2a/a(a+5)=1/a((a + 5) (a + 2) )}}} => since denominator cannot be equal to zero, {{{a((a + 5) (a + 2) )}}}  cannot be equal to zero too

so, {{{a((a + 5) (a + 2) ) =0}}} if {{{a=0}}}, {{{a=-5}}}, or{{{ a=-2}}}
therefore, we {{{exclude}}} these solutions


{{{((a-4)-2a)/a(a+5)=1/a((a + 5) (a + 2) )}}}



{{{(a-4-2a)/(cross(a)cross((a+5)))=1/(cross(a)cross((a + 5))(a + 2)) }}}


{{{(-a-4)=1/ (a + 2)}}}


{{{(-a-4)(a + 2)=1}}}


{{{(-a-4)(a + 2)-1=0}}}


{{{-a^2 - 6 a - 9 = 0}}}


{{{-(a + 3)^2 = 0}}}


double solution is:

{{{-(a + 3) = 0}}}

{{{-a-3=0}}}

{{{a=-3}}}

so, your solution is {{{highlight(a=-3)}}}

and {{{exclude}}} solutions are {{{a=-5}}}, or{{{ a=-2}}}