Question

If `a = (4xy)/(x + y)`, then `((a + 2x)/(a - 2x) + (a + 2y)/(a - 2y))` equals ______.

Options

• 1

• 2

• `1/2`

• none of these

Answer 1

If `a = (4xy)/(x + y)`, then `((a + 2x)/(a - 2x) + (a + 2y)/(a - 2y))` equals 2.

Explanation:

Substituting `a = (4xy)/(x + y)`, the two fractions simplify to `(x + 3y)/(y - x)` and `(3x + y)/(x - y)`. Their sum is 2, so the other numerical choices are incorrect.