What is the answer to (12x^2-4)/(4x-1)=3x ?

The answer to (12x^2-4)/(4x-1)=3x is x= 4/3

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(12x^2-4)/(4x-1)=3x

\frac{12 x ^{2} - 4}{4 x - 1} = 3 x

x = \frac{4}{3}

Decimal Notation

x = 1.33333 \dots

Solution steps

\frac{12 x ^{2} - 4}{4 x - 1} = 3 x

Multiply both sides by

4 x - 1

12 x^{2} - 4 = 3 x (4 x - 1)

Expand

3 x (4 x - 1) : 12 x^{2} - 3 x

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

Move

4

to the right side

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

Subtract

12 x^{2} - 3 x

from both sides

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

Simplify

3 x = 4

Divide both sides by

3

x = \frac{4}{3}

Verify Solutions

Find undefined (singularity) points:

x = \frac{1}{4}

Combine undefined points with solutions:

x = \frac{4}{3}

\frac{1}{x - 1} + \frac{3}{4 - x} = 0

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

\frac{32}{x} = \frac{4}{9}

- \frac{1}{( x - 1 ) ^{2}} = 0

\frac{16}{x} = - \frac{8}{5}

What is the answer to (12x^2-4)/(4x-1)=3x ?
The answer to (12x^2-4)/(4x-1)=3x is x= 4/3
Solve for x: (12x^2-4)/(4x-1)=3x
The solution is x= 4/3