anonymous
  • anonymous
(x-4)/(sqroot(x)-2) multiplied by its reciprocal
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
any expression multiplied by its reciprocal = 1 eg reciprocal of x = 1/x x * 1/x = 1
campbell_st
  • campbell_st
if the question is \[(x - 4)/(\sqrt{x} -2) \times (\sqrt{x} -2)/(x-4) \] the answer is 1.
anonymous
  • anonymous
yes

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

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