Answer:
[tex]m = -6 \ or \ m = -\frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{m^2+7m+6}+\frac{m+3}{m^2+7m+6}= \frac{5}{m+6}\\[/tex]
Simplifying the above equation we get:
Step 1: Solving for common denominator term we get;
[tex]\frac{1+m+3}{m^2+7m+6}= \frac{5}{m+6}\\\\\frac{m+4}{m^2+7m+6}= \frac{5}{m+6}[/tex]
Step 2: Multiplying denominators on both side we get;
[tex](m+4)(m+6)=5(m^2+7m+6)\\m^2+6m+4m+24 = 5m^2+35m+30\\m^2+10m+24 = 5m^2+35m+30\\5m^2+35m+30-m^2-10m-24=0\\4m^2+25m+6=0[/tex]
Step 3: Now we need to find the factors of m.
[tex]4m^2+25m+6=0\\4m^2+m +24m+6=0\\m(4m+1)+6(4m+1)=0\\(4m+1)(m+6)=0[/tex]
Step 4: Solving for both terms we get;
[tex]4m+1=0\\4m =-1\\m= - \frac{1}{4}[/tex]
Also,
[tex]m+6=0\\m=-6[/tex]
Hence [tex]m = -6 \ or \ m = -\frac{1}{4}[/tex]
