If (x = frac{y}{2}),evaluate(left(frac{x^{3}}{y^{3}}+frac{1}{2}right) div left(frac{1}{2} – frac{x^{2}}{y^{2}}right))
-
A.
5/8 -
B.
5/2 -
C.
5/32 -
D.
5/16
Correct Answer: Option B
Explanation
(x = frac{y}{2} )
(left(frac{x^{3}}{y^{3}}+frac{1}{2}right) div left(frac{1}{2} – frac{x^{2}}{y^{2}}right))
(frac{x^3}{y^3} + frac{1}{2} = (frac{y}{2})^{3} div y^{3} + frac{1}{2})
= (frac{y^{3}}{8} times frac{1}{y^3} + frac{1}{2})
= (frac{1}{8} + frac{1}{2})
= (frac{5}{8})
(frac{1}{2} – frac{x^2}{y^2} = frac{1}{2} – (frac{y}{2})^{2} div y^2))
= (frac{1}{2} – frac{y^2}{4} times frac{1}{y^2})
= (frac{1}{2} – frac{1}{4})
= (frac{1}{4})
(therefore left(frac{x^{3}}{y^{3}}+frac{1}{2}right) div left(frac{1}{2} – frac{x^{2}}{y^{2}}right) = frac{5}{8} div frac{1}{4})
= (frac{5}{2})