How do you solve #3/(x-3)-4=x/(x-3)# and check for extraneous solutions?

1 Answer
Apr 7, 2018

Answer:

#x=3# is extraneous solution, so original equation has no solution.

Explanation:

# 3/(x-3)-4=x/(x-3); x!=3# . Multiplying by #(x-3) # on both

sides we get, # 3-4(x-3)=x or 3-4x+12=x# or

# 5x =15 or x=3# Check : # 3/(3-3)-4=x/(3-3)#

#f(x)# is undefined at #x=3# Therefore, it cannot be a root of the

original equation. #x=3# extraneous solution, so original equation

has no solution. [Ans]