Question

Please explain answer to the math question in the picture thanks so much!

Answer 1

`m = -6 \ or \ m = -(1)/(4)`

Explanation:

Given

`(1)/(m^2+7m+6)+(m+3)/(m^2+7m+6)= (5)/(m+6)\\`

Simplifying the above equation we get:

Step 1: Solving for common denominator term we get;

`(1+m+3)/(m^2+7m+6)= (5)/(m+6)\\\\(m+4)/(m^2+7m+6)= (5)/(m+6)`

Step 2: Multiplying denominators on both side we get;

`(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`

Step 3: Now we need to find the factors of m.

`4m^2+25m+6=0\\4m^2+m +24m+6=0\\m(4m+1)+6(4m+1)=0\\(4m+1)(m+6)=0`

Step 4: Solving for both terms we get;

`4m+1=0\\4m =-1\\m= - (1)/(4)`

Also,

`m+6=0\\m=-6`

Hence
`m = -6 \ or \ m = -(1)/(4)`