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

Question

anonymous · Answer

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

campbell_st · Answer

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

anonymous · Answer

yes

anonymous · Answer

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

anonymous · Answer

but=by

anonymous · Answer

the opposite of the bottom?

anonymous · Answer

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

anonymous · Answer

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 · Answer

yes conjugate is the word i was looking for

anonymous · Answer

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

anonymous · Answer

glad to be of help

anonymous · Answer

thank you