How do you solve #1/(x+4)-2=(3x-2)/(x+4)#?

1 Answer
Nov 13, 2016

Answer:

#x=-1#

Explanation:

#1/(x+4) -2 = (3x-2)/(x+4)#

Get a common denominator by multiplying the 2nd term by #(x+4)/(x+4)#

#1/(x+4)-(2 * (x+4))/((x+4))= (3x-2)/(x+4)#

#1/(x+4)- ((2x+8))/(x+4)=(3x-2)/(x+4)#

Compare to a simple equation like #1/5 + 2/5 =x/5#
Because there is a common denominator, this can be solve with the numerators only #1 +2 =x#

Similarly, solve the equation using only the numerators.

#1-(2x+8)=3x-2#

Distribute the negative.

#1-2x-8=3x-2#

#-2x-7=color(white)(aa)3x-2#
#+2x+2=+2x+2#

#-5=5x#

#-5/5 =(5x)/5#

#-1=x#

When solving rational equations, it is important to check for extraneous solutions (solutions that "don't work" or result in division by zero).

#1/(-1+4)-2=frac{3(-1)-2}{-1+4}color(white)(aaa)#True