What is the answer to (3x)/(x-4)-2/x =3 ?

The answer to (3x)/(x-4)-2/x =3 is x=-4/5

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(3x)/(x-4)-2/x =3

\frac{3 x}{x - 4} - \frac{2}{x} = 3

x = - \frac{4}{5}

Decimal Notation

x = - 0.8

Solution steps

\frac{3 x}{x - 4} - \frac{2}{x} = 3

Multiply by LCM

3 x^{2} - 2 (x - 4) = 3 x (x - 4)

Expand

- 2 (x - 4) : - 2 x + 8

3 x^{2} - 2 x + 8 = 3 x (x - 4)

Expand

3 x (x - 4) : 3 x^{2} - 12 x

3 x^{2} - 2 x + 8 = 3 x^{2} - 12 x

Move

8

to the right side

3 x^{2} - 2 x = 3 x^{2} - 12 x - 8

Subtract

3 x^{2} - 12 x

from both sides

3 x^{2} - 2 x - (3 x^{2} - 12 x) = 3 x^{2} - 12 x - 8 - (3 x^{2} - 12 x)

Simplify

10 x = - 8

Divide both sides by

10

x = - \frac{4}{5}

Verify Solutions

Find undefined (singularity) points:

x = 4, x = 0

Combine undefined points with solutions:

x = - \frac{4}{5}

x + \frac{1}{x} = 3 \frac{11}{14}

(x - 2)^{- 1} = x^{- 1} + x

\frac{1}{x} + x = 2

\frac{1}{x} + x = 5

\frac{3}{x} = x

What is the answer to (3x)/(x-4)-2/x =3 ?
The answer to (3x)/(x-4)-2/x =3 is x=-4/5
Solve for x: (3x)/(x-4)-2/x =3
The solution is x=-4/5