## anonymous 4 years ago (x-4)/(sqroot(x)-2) multiplied by its reciprocal

1. anonymous

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

2. campbell_st

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

3. anonymous

yes

4. anonymous

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

5. anonymous

but=by

6. anonymous

the opposite of the bottom?

7. anonymous

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

8. 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)

9. anonymous

yes conjugate is the word i was looking for

10. anonymous

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

11. anonymous

12. anonymous

thank you

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