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

2 Answers
Sparrow ยท Alan P.
Jun 5, 2018

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

Mark D.
Jun 5, 2018

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

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