Jazmine Sweeney

2022-04-25

Simplifying fractions - Ending up with wrong sign

I've been trying to simplify this

$1-\frac{1}{n+2}+\frac{1}{(n+2)(n+3)}$

to get it to that

$1-\frac{(n+3)-1}{(n+2)(n+3)}$

but I always end up with this

$1-\frac{(n+3)+1}{(n+2)(n+3)}$

Any ideas of where I'm going wrong? Wolfram Alpha gets it to correct form but it doesn't show me the steps (even in pro version)

Thanks

I've been trying to simplify this

to get it to that

but I always end up with this

Any ideas of where I'm going wrong? Wolfram Alpha gets it to correct form but it doesn't show me the steps (even in pro version)

Thanks

foireatoutmtw

Beginner2022-04-26Added 15 answers

Everywhere there is a minus sign, replace it with plus a negative.

So with your original expression, try instead simplifying

$1+\frac{-1}{n+2}+\frac{1}{(n+2)(n+3)}$

and you should be much less prone to error.

So with your original expression, try instead simplifying

and you should be much less prone to error.

Larry Hogan

Beginner2022-04-27Added 20 answers

You just have the problem that while

$x-y+z=x-(y-z)$

you are instead writing:

$x-y+z=x-(y+z)$

you are instead writing:

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