#(x-9)/(x+4)=3#?

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Answer 1 · 2018-04-26T17:53:30

#x=-21/2#

#(x-9)/(x+4)=3# #/*(x+4)# to get rid of the fraction

#x-9=3*(x+4)#

#x-9=3x+12#

#x-3x=12+9#

#-2x=21# #/*(-1)#

#2x=-21#

#x=-21/2#

Answer 2 · 2018-04-26T17:57:44

#x = -21/2#

We must begin by adding the domain restriction #x!=-4# because this would cause division by 0:

#(x-9)/(x+4)=3, x !=-4#

Now that we have assured that we are not inadvertently multiplying by 0, we can eliminate the denominator by multiplying both sides by #(x+4)#:

#x-9=3(x+4), x !=-4#

Use the distributive property:

#x-9=3x+12, x !=-4#

Add #9-3x# to both sides:

#-2x = 21, x!=-4#

We can drop the domain restriction because it is obvious that the solution will not violate it:

#-2x = 21#

Multiply both sides by #-1/2#:

#x = -21/2#