I am doing proof by induction for my discrete math class by I'm horrible at algebra and I can't figure this last part out. Thanks in advance for the advice.

I need to make: (10^k) -1 + (9)(10^k)

look like this: 10^(k+1) -1

I also need help with this one:

I need to make: 1 - 1/(k+1) + 1/(k+1)(k+2) (1 is numerator, rest is Denom)

look like this: 1 - 1/(k+2)