Question 10

# If $$\frac{1}{x}$$ is a positive fraction and $$\frac{1}{y}$$ is a negative fraction then which of the following statements are true(A) $$\frac{1}{x} + \frac{1}{y}$$ is positive(B) $$\frac{1}{x} - \frac{1}{y}$$ is positive(C) $$\frac{x - y}{xy}$$ is negative(D) $$\frac{1}{xy}$$ is positive(E) $$\frac{1}{x^2} - \frac{1}{y^2}$$ is positiveChoose the correct answer from the options given below:

Solution

It is given that $$\frac{1}{x}$$ is positive and $$\frac{1}{y}$$ is negative, this implies that x is positive and y is negative.

A) $$\frac{1}{x}\ +\ \frac{1}{y}$$ is positive, we know x is positive, and y is negative, but we cannot conclude which value is greater. Therefore, this may or may not be true.

B)$$\frac{1}{x}-\frac{1}{y}$$ is positive; we know that x is positive and y is negative. So this statement is definitely true.

C) $$\ \frac{\ x-y}{xy}$$= -($$\frac{1}{x}-\frac{1}{y}$$)

As $$\frac{1}{x}-\frac{1}{y}$$ is positive, $$\ \frac{\ x-y}{xy}$$ is negative and statement is true.

D) $$\frac{1}{xy}$$ is negative as x is positive and y is negative. Therefore, the statement is false.

E)$$\frac{1}{x^2}-\frac{1}{y^2}$$ is positive only when $$y^2>x^2$$, but we cannot conclude which value is greater. Therefore, this may or may not be true.

Only (B) and (C) are true.