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Calculus/simplifying fractions where with x (x is to the power of -1 or less)
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Question
i have two problems i have no idea what to do on, and i realy dont know what to call them, i do know i have to simplify them.
first is:
((1/x)-(1/5))
---------------
((1/x^2)-(1/25))
and it should come out to 5x/(x+5) but i have no idea how it got there
and one more,
9-x^-2
------- (divisor)
3+x^-1
which comes to (3x-1)/x
just incase you wana know
Ok, the majour rules that we will use when simplifying is :
1. a^2-b^2=(a-b)*(a+b)
a/b a
2. --- = ---
c bc
a ac
3. --- = ---
b/c b
a b ad+cd
4. --- + --- = --------
c d cd
Ok, let's get to work.
1/x - 1/5 (5-x)/(5x) (5-x)*(25x^2)
----------- = ---------- = ------------ =
1/x^2 - 1/25 (25-x^2)/(25x^2) (25-x^2)*(5x)
(5-x)*(5x)*(5x) 5x
-------------- = ---
(5-x)*(5+x)*(5x) 5+x
................................................
9-x^(-2) 9 - 1/x^2 (9x^2-1)x (3x-1)*(3x+1)*x
------- = --------- = --------- = ------------- =
3+x^(-1) 3 + 1/x (3x + 1)x^2 (3x+1)*x^2
3x-1
----
x
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| Comment | very very very quick answer, knew exactly what to do, went over the top to help me, gave me tons more that helped me on future problems and saved my life! | ||
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