Alright, I need help solving what is probably an easy problem. I need to rationalise the numerator of
((1/√x)1)/(x1)
I tried multiplying by ((1/√x)+1)/((1/√x)+1), but it just made a mess of the denominator.
Calculus issues
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Re: Calculus issues
try combining 1/sqrt(x)1 into one fraction first.
Re: Calculus issues
Wait, nevermind, I lost my train of thought. Derp.
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Re: Calculus issues
MidsizeBlowfish wrote:try combining 1/sqrt(x)1 into one fraction first.
It comes out much nicer if you rationalise the denominator of the 1/sqrt(x) part first, then combine everything into one fraction.
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Re: Calculus issues
Sadly I think more often than previous the first time people are encountering rationalizing the denominator is in calculus; what's even sadder is that after calculus, it's rarely ever used again in math classes.
What I like to do is get everything in the form of exponents first, so something like:
((2/(root(2x))2)/(x+3) could be written as: (root(2)^2/root(2)root(x)+(iroot(2))^2)/(x+3), then simplified a bit to:
(root(2)/root(x)+i^2root(2))/(x+3) to (root(2)[(root(x)root(2)]^1)(x+3)^1 = root(2)[root(x)(x+3)root(2)(x+3)]^1
= root(2)/[(x^3/2)+3root(x)root(2)x3root(2)] = 1/[x^3+(3root(x)/root(2))x3] = [x^3x+3root(x)/root(2)3]^1 and I think that's as simplified as it gets, yours should look a bit nicer though, since more things will divide out evenly, mine was actually quite a mess, but I didn't want to use anything I thought you might get in an assignment.
What I like to do is get everything in the form of exponents first, so something like:
((2/(root(2x))2)/(x+3) could be written as: (root(2)^2/root(2)root(x)+(iroot(2))^2)/(x+3), then simplified a bit to:
(root(2)/root(x)+i^2root(2))/(x+3) to (root(2)[(root(x)root(2)]^1)(x+3)^1 = root(2)[root(x)(x+3)root(2)(x+3)]^1
= root(2)/[(x^3/2)+3root(x)root(2)x3root(2)] = 1/[x^3+(3root(x)/root(2))x3] = [x^3x+3root(x)/root(2)3]^1 and I think that's as simplified as it gets, yours should look a bit nicer though, since more things will divide out evenly, mine was actually quite a mess, but I didn't want to use anything I thought you might get in an assignment.
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