### Home > PC > Chapter 10 > Lesson 10.1.1 > Problem10-12

10-12.

Multiple Choice: I have two “funny rules” in mind. Suppose $A◊B = \left(A + B\right)^{ 2}$ and $AΔB = A^{2} − B^{2}$. Then $\frac { x ◊ y } { x \Delta y }=$ ?

1. $\frac { x ^ { 2 } + y ^ { 2 } } { x ^ { 2 } - y ^ { 2 } }$

2. $\frac { x + y } { x - y }$, for all values of $x$ and $y$

3. $\frac { x + y } { x - y }$, for $x ≠ +y$

4. none of the above

Note: This type of problem appears regularly on college entrance tests such as the SAT and ACT.

$\frac{(x+y)^2}{x^2-y^2}$