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Simplify. Is the simplified expression equivalent to the original, or is it frontin'?

The expression factors as .

Canceling the factor of (2x + 3) gives us .

This expression is not equivalent to the original expression, since we can evaluate at but we cannot evaluate the original expression at . Don't take our word for it, try it and see. The verdict is in: frontin'. We knew it.

Example 2

Simplify. Is the simplified expression equivalent to the original?

This expression factors as .

We can cancel one factor of (x + 1) from the numerator and denominator to find .

In this case, the original expression and its simplified version are equivalent. Neither expression can be evaluated at x = -1, and for every other value of x the two expressions will evaluate to the same number. These two might have been separated at birth. That mole on their left buttocks is a dead giveaway.