Why is 1-1/((n+1))+1/((n+1)(n+2)) = 1-((n+2)-1)/((n+1)(n+2))?

Kailey Vargas 2022-09-13 Answered
Why is 1 1 ( n + 1 ) + 1 ( n + 1 ) ( n + 2 ) = 1 ( n + 2 ) 1 ( n + 1 ) ( n + 2 ) ?
This is a step during a mathematical induction inside a textbook example I don't get
Also, if anyone has some good online resources to practice this sort of stuff, I'd be eternally grateful!
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Answers (1)

Savanah Morton
Answered 2022-09-14 Author has 15 answers
Because
1 1 n + 1 + 1 ( n + 1 ) ( n + 2 ) = 1 n + 2 ( n + 1 ) ( n + 2 ) + 1 ( n + 1 ) ( n + 2 ) = 1 ( n + 2 ( n + 1 ) ( n + 2 ) 1 ( n + 1 ) ( n + 2 ) ) = 1 ( ( n + 2 ) 1 ( n + 1 ) ( n + 2 ) ) = 1 ( n + 2 ) 1 ( n + 1 ) ( n + 2 )

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