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

2 Answers
Jun 5, 2018

Answer:

Assuming the question really was "solve for "#x#:
#color(white)("XXX")x=-3#

Explanation:

1 Multiply both sides by the Least Common Denominator [namely #x(x-1)#]
#color(white)("XXX")3x+1=2(x-1)#

2 Simplify
#color(white)("XXX")3x+1=2x-2#

3 Subtract #2x# from both sides
#color(white)("XXX")3x+1-2x=-2#

4 Simplify #3x+1-2x# to #x+1#
#color(white)("XXX")x+1=-2#

5 Subtract #1# from both sides
#color(white)("XXX")x=-2-1#

6 Simplify
#color(white)("XXX")x=-3#

Jun 5, 2018

Answer:

#x=-3#

Explanation:

Multiply the first fraction by #x#

#[3x+1]/[x(x-1)]=2/x#

Now multiply both sides by #x(x-1)# to remove the fractions

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

#3x+1=2x-2#

subtract #2x# from both sides

#x+1=-2#

subtract 1 from both sides