Question

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

Answer 1

any expression multiplied by its reciprocal = 1
eg reciprocal of x = 1/x
x * 1/x = 1

Answer 2

if the question is \[(x - 4)/(\sqrt{x} -2) \times (\sqrt{x} -2)/(x-4) \] the answer is 1.

Answer 3

yes

Answer 4

i think i used the wrong term... i have to multiply but the opposite of the bottom

Answer 5

but=by

Answer 6

the opposite of the bottom?

Answer 7

ya so its (x-4)/(sqroot(x)-2)*(sqroot(x)+2)/(sqroot(x)+2)

Answer 8

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)

Answer 9

yes conjugate is the word i was looking for

Answer 10

the (x-4)'s cancel out and you're left with sqrtx + 2

Answer 11

glad to be of help

Answer 12

thank you