m2+7m+10=(m+5)(m+2); 3m+15=3(m+5).
m/(3m+15)-1/(m2+7m+10)=
(1/(m+5))(m/3-1/(m+2))=
(1/(m+5))(m(m+2)-3)/(3(m+2))=
(1/(m+5))(m2+2m-3)/(3(m+2))=
(m+3)(m-1)/(3(m+2)(m+5).
(m-1)/(2(m+2))=(m+3)(m-1)/(3(m+2)(m+5)),
1/(2(m+2))=(m+3)/(3(m+2)(m+5)),
½=(m+3)/(3m+15),
3m+15=2(m+3)=2m+6,
m=6-15=-9.
CHECK
LHS:
(m-1)/(2m+4)=(-10)/(-18+4)=5/7.
RHS:
m/(3m+15)-1/(m2+7m+10)=(-9)/(-12)-1/(81-63+10)=¾-1/28=21/28-1/28=20/28=5/7.
LHS=RHS✔️