How do I simplify this into a single logarithm

The problem is 1/3ln (x+2)^3 + ½[ln x – ln(x^2 + 3x + 2)^2]

The correct answer should be ln(√x) / x+1

What are the steps in between?

1/3ln (x+2)^3 + ½[ln x – ln(x^2 + 3x + 2)^2]
= 1/3ln (x+2)^3 + ½ln x – ½ln(x^2 + 3x + 2)^2
= ln (x+2)^(3/3) + ln x^½ - ln (x^2 + 3x + 2)^(2/2)
= ln (x + 2) + ln (√x) - ln (x^2 + 3x + 2)
= ln (x + 2) + ln (√x) - ln ((x + 2)(x + 1)
= ln [(x + 2)(√x) / (x + 2)(x + 1)]
= ln [(√x) / (x + 1)]