How do you find the excluded value and simplify # (x+3)/(x^2+7x+12)#?

1 Answer
Nov 2, 2017

Answer:

#"see explanation"#

Explanation:

#"the excluded values are the values of x that make"#
#"the denominator of the rational function equal zero"#
#"as this would make the rational function "color(blue)"undefined"#

#"to find the excluded values equate the denominator"#
#"to zero and solve for x"#

#"solve "x^2+7x+12=0#

#"the factors of 12 which sum to + 7 are + 3 and + 4"#

#rArr(x+3)(x+4)=0#

#"equate each factor to zero and solve for x"#

#x+3=0rArrx=-3#

#x+4=0rArrx=-4#

#x=-3,x=-4larrcolor(red)" are the excluded values"#

#"to simplify "color(blue)"cancel common factors"" on the"#
#"numerator/denominator of the rational function"#

#rArr(x+3)/((x+3)(x+4))#

#=(cancel((x+3))^1)/(cancel((x+3))^1(x+4))=1/(x+4)#