Question

Arrange the expressions in ascending order of their values when x=-2

Answer 1

Answer:

The expressions in ascending order would be:

$\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}$

At x = -2

Explanation:

First, we will evaluate the given expressions at x = -2

1- The first expression:

$\frac{x^2}{1-2x}=\frac{(-2)^2}{1-2(-2)}=\frac{4}{5}$

2- The second expression:

$\frac{x^2-1}{1-2x}=\frac{(-2)^2-1}{1-2(-2)}=\frac{3}{5}$

3- The third expression:

$\frac{2x^2+x}{2}=\frac{2(-2)^2+(-2)}{2}=3$

4- The fourth expression:

$\frac{3x^2+1}{2(x-1)}=\frac{3(-2)^2+1}{2(-2-1)}=-\frac{13}{6}$

Then, we will arrange the values in an ascending order:

$-\frac{13}{6} < \frac{3}{5} < \frac{4}{5} < 3$

Finally, we arrange the expressions based on the value arrangement:

$\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}$

Hope this helps :)