(m-1/2m+4) = ((m/3m+15)-(1/m^2+7m+10))

Question

please help solve and check

Answer 1

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✔️