Simplify completely: `(x^2+12x+35)/(3x+15)` .Explain how to simplify completely. Please and thank you.
A rational expression is simplified if there are no common factors in the numerator and denominator.
(1) Factor numerator and denominator:
(2) Notice that (x+5) appears as a factor in both numerator and denominator. Cancelling this common factor yields:
(3) Note that in the original expression, x=-5 is not in the domain, as this leads to a division by zero. In the final expression in (2) there is no such restriction.
So: For `x!=5` the expression `(x^2+12x+35)/(3x+15)` is equivalent to `(x+7)/3` , which is fully simplified.