(x-4)/(sqroot(x)-2) multiplied by its reciprocal

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(x-4)/(sqroot(x)-2) multiplied by its reciprocal

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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any expression multiplied by its reciprocal = 1 eg reciprocal of x = 1/x x * 1/x = 1
if the question is \[(x - 4)/(\sqrt{x} -2) \times (\sqrt{x} -2)/(x-4) \] the answer is 1.
yes

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Other answers:

i think i used the wrong term... i have to multiply but the opposite of the bottom
but=by
the opposite of the bottom?
ya so its (x-4)/(sqroot(x)-2)*(sqroot(x)+2)/(sqroot(x)+2)
hmm maybe you want to simplify by rationalising the denominator i e multoplying top and bottom by the conjugate of sqrtx - 2 which is sqrtx + 2 so its (x-4)*(sqrtx + 2) (x-4)(sqrtx+2) -------------- = ------------ = sqrtx + 2 (sqrtx-2)(sqrtx+2) ( x - 4)
yes conjugate is the word i was looking for
the (x-4)'s cancel out and you're left with sqrtx + 2
glad to be of help
thank you

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