Question

x^3-1/x^2-1

Answer 1

What's the question?

Answer 2

Simplify the rational expression. If the rational expression cannot be simplified, so state

Answer 3

Factor both numerator and denominator

Answer 4

Denominator:
\[x^2-1=(x+1)(x-1)\]

Answer 5

For numerator, let \(f(x)=x^3-1\)
When x=1, f(x)=0, then (x-1) is a factor of f(x)
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That simplifies the numerator to \((x-1)(x^2 + ? + ? )\)

Answer 6

You could find the missing quadratic equation by dividing \(x^3-1\) by \(x-1\)

You should get \[(x-1) \left(x^2+x+1\right)\]For the numerator.
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So
\[\frac{(x-1) \left(x^2+x+1\right)}{(x-1)(x+1)} \\ =\frac{\cancel{(x-1)} \left(x^2+x+1\right)}{\cancel{(x-1)}(x+1)} \]