Solve the equation and show the check of the potential answers

Question

4n+5/n+3-1/n+4=1/n^2+7n+12

Answer 1

OK, you left some parentheses out, but I think the equation is:

 

(4n+5)/(n+3) - 1/(n+4) = 1/(n²+7n+12)

 

Note that n²+7n+12 can be factored and equals (n+4)(n+3):

 

(4n+5)/(n+3) - 1/(n+4) = 1/(n+4)(n+3)

 

Multiply both sides by (n+4)(n+3):

 

(4n+5)(n+4) - (n+3) = 1

4n² + 16n + 5n + 20 - n -3 -1 = 0

4n² + 20n + 16 = 0

4(n² + 5n + 4) = 0

 

Can you finish it from here?  The  quadratic in the parentheses can be factored, or you can always use the quadratic formula.