what is the answer to 3/2n^2+10n+8 = n/2n+2 + 1/n+1

Question

The answer is not n/2 +1. Please help me!

Answer 1

2n²+10n+8=2(n+1)(n+4). Multiply through by this:

3=n(n+4)+2(n+4),

3=n²+4n+2n+8=n²+6n+8,

n²+6n+5=0=(n+1)(n+5), and n=-1 or -5.

However, n=-1 would make all the denominators zero. So this solution must be rejected, because the fractions cannot be defined. The only solution is n=-5.

CHECK

Plug in n=-5:

3/8=(-5)/(-8)+1/(-4)=5/8-1/4, which is true, so n=-5 is the confirmed solution.