How do you simplify #(2x^2+6x+4)/(3x^2+9x+6)# and then find the excluded values?

1 Answer
Jim G.
Apr 4, 2017

#2/3#

Explanation:

The first step is to factorise the numerator/denominator.

Both have a #color(blue)"common factor"# that can be taken out.

#(color(blue)(2)(x^2+3x+2))/(color(blue)(3)(x^2+3x+2))#

#=(2(cancel(x^2+3x+2))^1)/(3(cancel(x^2+3x+2))^1)=2/3#

Excluded values are values of x that make the function #color(blue)" undefined"#

The denominator cannot equal zero as this would make the function undefined. Equating the denominator to zero and solving gives the values that x cannot be.

#"solve " x^2+3x+2=0#

#rArr(x+1)(x+2)=0rArrx=-1" or " x=-2#

#"Thus " x=-1" and " x=-2" are the excluded values"#

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