If (x^(3/2) - xy^(1/2) + x^(1/2)y - y^(3/2)) is divided by (x^(1/2) - y^(1/2)), the quotient is :

Question

If \((x^\frac32-xy^\frac12+x^\frac12y-y^\frac32)\) is divided by \((x^\frac12-y^\frac12)\), the quotient is :

(a) x + y 

(b) x – y 

(c) \(x^\frac12-y^\frac12\)

(d) x² - y²

Answer 1

(a) x + y

\((x^\frac32-xy^\frac12+x^\frac12y-y^\frac32)\)

= \(x(x^\frac12-y^\frac12) + y(x^\frac12-y^\frac12)\)

= (x + y) \((x^\frac12-y^\frac12)\)

∴ \((x^\frac32-xy^\frac12+x^\frac12y-y^\frac32)\) ÷ \((x^\frac12-y^\frac12)\)

= \(\frac{(x + y)(x^\frac12-y^\frac12)}{x^\frac12-y^\frac12}\) = (x + y)