What is the solution of this ? #x/(x-2) + 3=2/(x-2)#

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Answer 1 · 2018-05-22T18:41:48

x =2 is the algebraic answer to the equation but the algebraic answer is not allowed so there is no rational solution.

the solution is to multiply everything by (x -2) to remove the denominators and eliminate the fractional forms of the terms.

# (x-2) xx { (x)/(x-2)} + (x-2) xx 3 = {(x-2) xx {(2)/(x-2)}#

Multiplying everything (x-2) results in

# x + 3x -6 = 2 #

Combine the x terms and add six to both sides

# x + 3x -6 + 6 = 2 +6# This gives

#4x = 8#

Divide both sides by 4

# (4x)/4 = 8/4# the answer is

# x = 2 #

However (x-2) when x = 2 give # 2-2 = 0

Putting this into the equation gives

# 2/(2-2) +3 = 2/(2-2)#

which gives

# 2/0 + 3 = 2/0 # dividing by zero is undefined

this means that the only algebraic answer is undefined and is not allowed.