Question 20

Explanation

Given $-1 < x < 1$, with:

• $P = \frac{1 + x^4}{1 - x^2}$
• $Q = 1 + x^4$

Analyzing the range of x

For $-1 < x < 1$, we check the value of $1 - x^2$.

Since $x^2$ is always positive for $x \neq 0$, then:

Therefore:

Comparing P and Q

We divide $P$ by $Q$:

Now we analyze two cases:

Case 1: If $0 < 1 - x^2 < 1$

Then $\frac{1}{1 - x^2} > 1$, so $P > Q$.

Case 2: If $1 - x^2 = 1$ (i.e., when $x = 0$)

Then $\frac{1}{1 - x^2} = 1$, so $P = Q$.

Conclusion

Since the value of $x$ in the interval $-1 < x < 1$ can result in $P > Q$ (for $x \neq 0$) or $P = Q$ (for $x = 0$), the information provided is not sufficient to decide on one of the three options.