Question

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

Answer 1

`"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)`