factor x^-1/2 + x^5/2  TOPIC_SOLVED

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

factor x^-1/2 + x^5/2

Postby buddy on Wed Feb 25, 2009 10:20 pm

factor x^-1/2 + x^5/2
the -1/2 and 5/2 are powers
i dont see how anything comes out?
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Postby stapel_eliz on Wed Feb 25, 2009 11:01 pm

buddy wrote:factor x^-1/2 + x^5/2
the -1/2 and 5/2 are powers

To format this clearly, use grouping symbols:

. . . . .x^(-1/2) + x^(5/2)

You can also use the "sup" tags (from the formatting line above the message-entry box):

. . . . .x[sup]-1/2[/sup] + x[sup]5/2[/sup]

...displays as:

. . . . .x-1/2 + x5/2

buddy wrote:i dont see how anything comes out?

Nothing much does, actually... :roll:

Use exponent rules to convert the negative-powered term to a fraction:

. . . . .

. . . . .

You might find it easy, by the way, to convert the fractional powers to radical form, while you're doing your steps:

. . . . .

. . . . .

The common denominator is the square root of x, but of course you're not supposed to have radicals in the denominator, so let's "rationalize" that first:

. . . . .

. . . . .

Now the common denominator would be x, so:

. . . . .

. . . . .

The only common factor is the radical:

. . . . .

Factor the sum of cubes, and I think you're done! :D
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Re: factor x^-1/2 + x^5/2

Postby buddy on Wed Feb 25, 2009 11:35 pm

so its (square root of x)(1+x)(1+x+x^2)/x?
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  TOPIC_SOLVED

Postby stapel_eliz on Thu Feb 26, 2009 2:35 pm

Check your signs! There should be a "minus" somewhere in the factoring of the sum of cubes! :wink:
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