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Algebra fractions simplifying?
Please show step by step how:
[(A + 1)*((A/(A^2 + 1)) - (1/A))] / [2+(1/A)+A]
becomes:
[-1] / [(A + 1)(A^2 + 1)]
3 Answers
- LawrenceLv 64 years ago
Multiply by A/A...
[A*(A + 1)*((A/(A^2 + 1)) - (1/A))]
-----------------------------------------------------
[A*(2+(1/A)+A)]
Multiply out denominator...
[A*(A + 1)*((A/(A^2 + 1)) - (1/A))]
----------------------------------------------------
[A^2 + 2A + 1]
denominator simplifies...
[A*(A + 1)*((A/(A^2 + 1)) - (1/A))]
-----------------------------------------------------
(A+1)^2
The (A+1) term cancels leaving...
[A*((A/(A^2 + 1)) - (1/A))]
----------------------------------------
(A+1)
Multiply out numerator...
[(A^2)/(A^2 + 1) - 1]
-------------------------------
(A+1)
Replace -1 in numerator with
(A^2 + 1)/(A^2 + 1), then
[(A^2)/(A^2 + 1) - (A^2 + 1)/(A^2 + 1)]
-------------------------------
(A+1)
Which leaves...
[-1/(A^2 + 1)]
---------------------
(A+1)
Multiply by 1 in the form...
[1/(A+1)] / [1/(A+1)]
which then yields the desired answer of...
[ -1 / (A^2 + 1)(A+1) ]
- ?Lv 74 years ago
(A + 1)*((A/(A^2 + 1)) - (1/A))] / [2 + (1/A) + A]
= ((-1) (A + 1))/(A (A^2 + 1)) / ((A + 1)^2/A
= ((-1)/(A (A^2 + 1)) / ((A + 1)/A))
= -1/(A + 1) (A^2 + 1)
- alexLv 74 years ago
[(A + 1)*((A/(A^2 + 1)) - (1/A))]= (A+1)(A^2-(A^2+1) )/[A(A^2+1)]= -(A+1)/[A(A^2+1)]
and [2+(1/A)+A] =(A^2+2A+1)/A=(A+1)^2/A
hence { -(A+1)/[A(A^2+1)] }/{(A+1)^2/A} = { -(A+1)/[A(A^2+1)] }x{A/(A+1)^2} = ...
