I need help simplifying a rational expression.

Help me understand simplifying this rational expression?

• The problem is: x^2 + 6x +5 ---------------- x^2 - 25 The work is shown in the book as follows Step 1: (x+5)(x+1) -------------- (x+5)(x-5) No problem so far. Step 2: Factor out the (x+5)s. Still no problem. Step 3: The answer is: x + 1 ------- , x ≠ -5, x ≠ 5 x - 5 I understand that x cannot equal 5, because subtracting 5 from five would equal 0 and you can't have 0 in the denominator. I don't understand why you can't have -10 in the denominator, though! I'm really confused. The book has several problems in it and in some of them it seems to make sense, but in others it excludes numbers that would either make the numerator 0 (the text never indicates that this is not an option) or that are opposite of the number that would make the denominator 0. Are there rules about simplifying rational expressions that are not included in the text? Thanks!

• Answer:

  It's not that you can't have -10 in the denominator - remember you reduced the original expression. The original expression's denominator was x^2 - 25. The square of -5 is also 25, so x=-5 would also result in a zero denominator.