Find the values of 'a' for which `-3<(x^2+ax-2)/(x^2+x+1)<2` is valid for all real `x.`

Explanation

To solve the inequality \(-3 < \frac{x^2 + ax - 2}{x^2 + x + 1} < 2\) for all real \(x\), we will break it down into two parts:

1. **Part 1:** \(-3 < \frac{x^2 + ax - 2}{x^2 + x + 1}\)
2. **Part 2:** \(\frac{x^2 + ax - 2}{x^2 + x + 1} < 2\)

### Step 1: Solve Part 1

Starting with the first inequality:
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