Logarithmic differentiation issue

Trying to understand a solution I was given to a problem I was told to use logarithmic differentiation on.

$$1/x(x+1)(x+2)$$

and I know that

$$log((ab)/c)=log(a)+log(b)-log(c)$$

So I tried to use that rule here and did:

$$ln(a)-ln(b)-ln(c)$$

and got:

$$ln(1)-ln(x(x+1)-ln(x(x+2)$$<>rbwhich simplifies to:

$$0-ln({x}^{2}+x)-ln({x}^{2}+2x)$$

and then I look at the solution which gives:

$$y\u2018=(1/(x(x+1)(x+2)))\ast (1/x+1/(x+1)+1/(x+2))$$

I'm just kind of confused on what I am doing wrong.

Trying to understand a solution I was given to a problem I was told to use logarithmic differentiation on.

$$1/x(x+1)(x+2)$$

and I know that

$$log((ab)/c)=log(a)+log(b)-log(c)$$

So I tried to use that rule here and did:

$$ln(a)-ln(b)-ln(c)$$

and got:

$$ln(1)-ln(x(x+1)-ln(x(x+2)$$<>rbwhich simplifies to:

$$0-ln({x}^{2}+x)-ln({x}^{2}+2x)$$

and then I look at the solution which gives:

$$y\u2018=(1/(x(x+1)(x+2)))\ast (1/x+1/(x+1)+1/(x+2))$$

I'm just kind of confused on what I am doing wrong.