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

Question

1341 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-16T13:37:58

See the entire solution process below:

We can factor the denominator as:

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

We can than simplify this expression as:

#color(red)(cancel(color(black)(x + 3)))/((color(red)(cancel(color(black)(x + 3))))(x + 4)) = 1/(x + 4)#

To find the excluded values we need to solve for the denominator equal to #0#:

Exclusion 1)

#x + 3 = 0#

#x + 3 - 3 = 0 - 3#

#x + 0 = -3#

#x = -3#

Exclusion 2)

#x + 4 = 0#

#x + 4 - 4 = 0 - 4#

#x + 0 = -4#

#x = -4#

The excluded values are #-3# and #-4#