Question 747562
Don't be fooled by how complicated this monster of an equation looks. We'll methodically simplify it until we can solve.

First we move all terms with the same denominator to the same side
{{{
((m+2)/(m^2+8m+15))-((m+2)/(m^2+8m+15))-((2)/(m^2+10m+25))=(m-2)/(m^2+8m+15)-((m+2)/(m^2+8m+15))
}}}




which becomes


{{{
(-2)/(m^2+10m+25)=((m-2)-((m+2)))/(m^2+8m+15)
}}}




Our next step is to factor denominators and simplify numerators



{{{
(-2)/((m+5)(m+5))=(-4)/((m+5)(m+3))
}}}


After we divide out a common factor of -2/(m+5) we get the proportion:


{{{
1/(m+5)=2/(m+3)
}}}

Now we cross multiply and solve for m


{{{
m+3=2(m+5)
}}}


{{{m+3=2m+10}}}
{{{m-m+3-10=2m-m+10-10}}}
{{{-7=m}}}


Therefore m=-7







:)