How do you simplify and find the restrictions for #1/(x+4) -2#?

1 Answer
Jan 31, 2017

# -(2x-9)/(x+4)#

Restriction (excluded value) is: #x=-4#

Explanation:

You are not allowed (undefined) to divide by 0 so #x+4 !=0#
means that the excluded value is #x=-4#

To solve this you need to 'force' the - 2 to be something over #x+4#

#color(green)(1/(x+4)-[2xxcolor(red)(1)]#

But 1 = #(x+4)/(x+4)#

#color(green)(1/(x+4)-[2xxcolor(red)((x+4)/(x+4))])#

#color(green)(1/(x+4)-color(white)(.)(2color(red)((x+4)))/(color(red)(x+4)))#

#color(green)((1-2x+8)/(x+4))#

#color(green)((-2x+9)/(x+4))#

But #-2x+9" is the same as "-(2x-9)# giving

#color(green)((-(2x-9))/(+(x+4)) = -(2x-9)/(x+4))#