# How do you simplify #(2z^2 - 11z + 15)/(z^2 - 9)#?

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First we need to split the middle term

After splitting... you'll get

This is a law of exponents

Factorize

You get

You are left with

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To simplify the expression (2z^2 - 11z + 15)/(z^2 - 9), we can factor both the numerator and the denominator. The numerator can be factored as (2z - 3)(z - 5), and the denominator can be factored as (z - 3)(z + 3).

Therefore, the expression simplifies to (2z - 3)(z - 5)/(z - 3)(z + 3).

Next, we can cancel out the common factors of (z - 3) in the numerator and denominator.

The simplified expression is (2z - 3)(z - 5)/(z + 3).

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