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

The answer to (3x^2-4)/x =3(x-4) is x= 1/3

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

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

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

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

Multiply both sides by

x

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

Expand

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

3 x^{2} - 4 = 3 x^{2} - 12 x

Move

4

to the right side

3 x^{2} = 3 x^{2} - 12 x + 4

Subtract

3 x^{2} - 12 x

from both sides

3 x^{2} - (3 x^{2} - 12 x) = 3 x^{2} - 12 x + 4 - (3 x^{2} - 12 x)

Simplify

12 x = 4

Divide both sides by

12

x = \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{3}

y, \frac{x}{y} = x

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

x^{2} + \frac{1}{x} = 0, x > 0

r, S = \frac{a}{a - r}

\frac{3 x + 5}{2} + \frac{1}{x} = 0

What is the answer to (3x^2-4)/x =3(x-4) ?
The answer to (3x^2-4)/x =3(x-4) is x= 1/3
Solve for x: (3x^2-4)/x =3(x-4)
The solution is x= 1/3