How do you simplify (sqrtx+sqrty)/(sqrtx-sqrty)?

2 Answers
Narad T.
Feb 9, 2017

The answer is =(x+y+2sqrt(xy))/(x-y)

Explanation:

Multiply numerator and denominator by sqrtx+sqrty

So,

(sqrtx +sqrty)/(sqrtx-sqrty)

=(sqrtx +sqrty)/(sqrtx-sqrty)*(sqrtx+sqrty)/(sqrtx+sqrty)

=(x+y+2sqrt(xy))/(x-y)

George C.
Feb 9, 2017

(sqrt(x)+sqrt(y))/(sqrt(x)-sqrt(y)) = (x+2sqrt(xy)+y)/(x-y)

Explanation:

To "rationalise" the denominator, multiply by its radical conjugate sqrt(x)+sqrt(y) as follows:

(sqrt(x)+sqrt(y))/(sqrt(x)-sqrt(y)) = ((sqrt(x)+sqrt(y))(sqrt(x)+sqrt(y)))/((sqrt(x)-sqrt(y))(sqrt(x)+sqrt(y))

color(white)((sqrt(x)+sqrt(y))/(sqrt(x)-sqrt(y))) = (x+2sqrt(x)sqrt(y)+y)/(x-y)

color(white)((sqrt(x)+sqrt(y))/(sqrt(x)-sqrt(y))) = (x+2sqrt(xy)+y)/(x-y)

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