 # 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 $1-\frac{1}{\left(n+1\right)}+\frac{1}{\left(n+1\right)\left(n+2\right)}=1-\frac{\left(n+2\right)-1}{\left(n+1\right)\left(n+2\right)}?$
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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Because
$1-\frac{1}{n+1}+\frac{1}{\left(n+1\right)\left(n+2\right)}\phantom{\rule{0ex}{0ex}}=1-\frac{n+2}{\left(n+1\right)\left(n+2\right)}+\frac{1}{\left(n+1\right)\left(n+2\right)}\phantom{\rule{0ex}{0ex}}=1-\left(\frac{n+2}{\left(n+1\right)\left(n+2\right)}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)\phantom{\rule{0ex}{0ex}}=1-\left(\frac{\left(n+2\right)-1}{\left(n+1\right)\left(n+2\right)}\right)\phantom{\rule{0ex}{0ex}}=1-\frac{\left(n+2\right)-1}{\left(n+1\right)\left(n+2\right)}\phantom{\rule{0ex}{0ex}}$

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