If y/2=x

Question

Calculate (x/y+1/2)-(1/2-x/ysquare)

Answer 1

To simplify the expression:

(x/y + 1/2) - (1/2 - x/y^2)

Let's substitute the given equation y/2 = x into the expression:

(x/y + 1/2) - (1/2 - x/y^2)

= ((y/2) / y + 1/2) - (1/2 - (y/2) / y^2)

Simplifying inside the parentheses:

= ((1/2) + 1/2) - (1/2 - (1/2) / y^2)

= (1) - (1/2 - 1/2y^2)

Now we can find a common denominator and combine like terms:

= 1 - (y^2 - 1) / (2y^2)

= 1 - y^2 + 1 / (2y^2)

= -y^2 + 2 / (2y^2)

= (-y^2 + 2) / (2y^2)