Simplify the difference.

Question

y/2y+4−3/y+2

Answer 1

To simplify the difference, we need to find a common denominator for the two fractions.

y/2y + 4 = y / 2y + 4 * 1 = y / 2y + 4 * 2 / 2 = y / 2y + 8 / 2y

3/y + 2 = 3 / y + 2 * y / y = 3y / y^2 + 2y

Now, we have:

y / 2y + 8 / 2y - 3y / y^2 + 2y

To find a common denominator, we multiply the numerators and denominators of the two fractions by the missing factors:

y^2 / 2yy^2 + 8y / 2yy^2 - 3y^2 / y^2x + 2y

Now, our expression is:

(y^2 + 8y - 3y^2) / 2yy^2 + 2y

Simplifying the numerator:

(-2y^2 + 8y) / 2yy^2 + 2y

Combine like terms:

(8y - 2y^2) / 2yy^2 + 2y

So, the simplified difference is: (8y - 2y^2) / 2yy^2 + 2y.