Question

Solve the equation

3x/3x-1 + 2/x = 1

Answer 1

x= 2/7

Explanation:

Multiply both sides by the common denominator

3x^2 +6x−2=3x^2 −x

Move everything to the left side.

3x^2+6x-2-3x^2+x=0

Simply.

7x-2=0

Separate the cosntants and variables.

7x=0+2

Add or subtract zero

7x=2

Then divide both sides by 7.

7x/7=2/7

Cancel out common factors in the numerator and denominator

x=2/7

Answer 2

x = 2/7

Explanation:

You want to solve the equation 3x/(3x-1) + 2/x = 1.

Solution

It works nicely to subtract 1 from both sides, then simplify.

`(3x)/(3x-1)+(2)/(x)=1\\\\(3x)/(3x-1)\cdot(x)/(x)+(2)/(x)\cdot(3x-1)/(3x-1)-(x(3x-1))/(x(3x-1))=0\\\\(3x^2+6x-2-3x^2+x)/(x(3x-1))=0\qquad\text{combine terms}\\\\(7x-2)/(x(3x-1))=0\qquad\text{simplify}\\\\7x-2=0\qquad\text{expression is 0 when numerator is 0}\\\\\boxed{x=(2)/(7)}\qquad\text{add 2, divide by 7}`

__

Additional comment

The values x=0 and x=1/3 would make the denominator zero, so are excluded from the domain of the equation. By working the problem this way, we ensure that extraneous solutions do not present themselves.