Better Students Ask More Questions.
Reduce to lowest terms `x^2 - 16` over `x^2 + 8x + 16`
1 Answer | add yours
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)`
The result is `(x-4)/(x+4)`
Posted by ishpiro on June 25, 2013 at 2:48 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.