Let's simplify the given expression step by step.
1) Simplify 1/2x^0.5:
1/2x^0.5 = 1/2 * sqrt(x) = sqrt(x)/2
2) Simplify 3y^0.5:
3y^0.5 = 3 * sqrt(y)
3) Simplify - 1/2x^0.5:
4) Simplify - 3x^0.5:
5) Simplify (2x-9/2y):
= 2x - 9/(2y)
Using the above simplifications, we substitute them back into the given expression:
(sqrt(x)/2) + 3sqrt(y) - sqrt(x)/2 - 3sqrt(x) * (2x - 9/(2y))
This expression can be further simplified by expanding the last term using the distributive property:
(sqrt(x)/2) + 3sqrt(y) - sqrt(x)/2 - 3sqrt(x)2x + 3sqrt(x)*(9/(2y))
Which simplifies to:
3sqrt(y) - 6xsqrt(x) + 27/(2sqrt(y))
Therefore, the simplified expression is:
Let's simplify the given expression step by step.
1) Simplify 1/2x^0.5:
1/2x^0.5 = 1/2 * sqrt(x) = sqrt(x)/2
2) Simplify 3y^0.5:
3y^0.5 = 3 * sqrt(y)
3) Simplify - 1/2x^0.5:
1/2x^0.5 = - sqrt(x)/24) Simplify - 3x^0.5:
3x^0.5 = - 3* sqrt(x)5) Simplify (2x-9/2y):
= 2x - 9/(2y)
Using the above simplifications, we substitute them back into the given expression:
(sqrt(x)/2) + 3sqrt(y) - sqrt(x)/2 - 3sqrt(x) * (2x - 9/(2y))
This expression can be further simplified by expanding the last term using the distributive property:
(sqrt(x)/2) + 3sqrt(y) - sqrt(x)/2 - 3sqrt(x)2x + 3sqrt(x)*(9/(2y))
Which simplifies to:
3sqrt(y) - 6xsqrt(x) + 27/(2sqrt(y))
Therefore, the simplified expression is:
3sqrt(y) - 6xsqrt(x) + 27/(2sqrt(y))