How do you simplify and find the restrictions for #3/(x-4)-7#?

1 Answer
Aug 16, 2017

Restriction: #color(red)(x!=4)#
Simplification (maybe): #color(blue)((31-7x)/(x-4))#

Explanation:

Since division by #0# is undefined.
#x-4!=0color(white)("xxx")rarrcolor(white)("xxx")x!=4#

What is considered a "simplification" is more problematic.
Here is one possibility:
#color(white)("XXX")3/(x-4)-7#

#color(white)("XXXXXX")=3/(x-4)-(7(x-4))/(x-4)#

#color(white)("XXXXXX")=3/(x-4)-(7x-28)/4#

#color(white)("XXXXXX")=(3-7x+28)/(x-4)#

#color(white)("XXXXXX")=(31-7x)/(x-4)#