Proving 1 - 1/(x+1)! + (x+1)/(x+2)! = 1 - 1/(x+2)!

[solidus_E]

Homework Statement

trying to prove left-hand side = right-hand side

this is where I'm stuck:

$$1 - [1 / (x+1)!] + [(x+1) / (x+2)!] = 1 - [1 / (x+2)!]$$

Homework Equations

The Attempt at a Solution

i tried this but can't get anywhere

get a common demoninator:
1 - [(x+2)! + (x+1)*(x+1)! / (x+1)!*(x+2)!]

anyone seeing what I'm not seeing?

 

[neutrino]

get a common demoninator:
1 - [(x+2)! + (x+1)*(x+1)! / (x+1)!*(x+2)!]

That should be a minus.

Pull out the (x+1)! from the numerator of the second term and simplify.

 

[brh2113]

A useful trick is to write (x+2)! as (x+2)(x+1)!