# How do you prove #(tan^3x - 1) /( tanx - 1) = tan^2x + tanx + 1#?

as directed below

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To prove ( \frac{{\tan^3 x - 1}}{{\tan x - 1}} = \tan^2 x + \tan x + 1 ), we can follow these steps:

- Rewrite the numerator ( \tan^3 x - 1 ) as ( (\tan^2 x + \tan x + 1)(\tan x - 1) ) using polynomial division.
- Simplify the expression by canceling out common terms.
- Verify that the resulting expression is equal to ( \tan^2 x + \tan x + 1 ).

Performing these steps will demonstrate the equality between the given expression and ( \tan^2 x + \tan x + 1 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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