# Reduce to lowest terms `x^2 - 16` over `x^2 + 8x + 16`

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### 1 Answer

Reducing to lowest terms means dividing both denominator and numerator by the greatest common factor.

`x^2 - 16` over `x^2 + 8x + 16` can be written as a fraction:

`(x^2 - 16)/(x^2 + 8x + 16)`

Factor both numerator and denominator:

`x^2 - 16 = (x-4)(x+ 4)` because this is a difference of two squares

`x^2 + 8x + 16 = (x+2)(x+4)`

Therefore (x+ 4) is a common factor that can be canceled:

`(x^2 - 16)/(x^2 + 8x + 16) = ((x-4)(x+4))/((x+2)(x+4)) = (x-4)/(x+4)`

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**The result is** `(x-4)/(x+4)`