**Topic**

Let x and y be two real numbers that differ from -1. Which of the following conclusions is correct?

A. \(x + y + xy \ne – 1\)

B. \(x + y + xy = – 1\)

C. \(x + y \ne – 2\)

D. \(xy \ne – 1\)

**Solution method – See details**

Check each clause. Type the answer by giving an example.

**Detailed explanation**

We have: \(x \ne – 1 \Rightarrow x + 1 \ne 0\).

Similarly \(y + 1 \ne 0\). Therefore: \((x + 1)(y + 1) \ne 0\) or \(x + y + xy \ne – 1\)

**Choose A**.

C is wrong, for example \(x = 0,y = – 2\) satisfies but \(x + y = – 2\)

D is false, for example \(x = \frac{1}{2},y = – 2\) satisfies but \(xy = – 1\)