What is the answer to ((6x^2-12))/((3x-4))=2x ?

The answer to ((6x^2-12))/((3x-4))=2x is x= 3/2

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((6x^2-12))/((3x-4))=2x

\frac{( 6 x ^{2} - 12 )}{( 3 x - 4 )} = 2 x

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

\frac{( 6 x ^{2} - 12 )}{( 3 x - 4 )} = 2 x

Simplify

\frac{( 6 x ^{2} - 12 )}{( 3 x - 4 )} : \frac{6 x ^{2} - 12}{3 x - 4}

\frac{6 x ^{2} - 12}{3 x - 4} = 2 x

Multiply both sides by

3 x - 4

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

Expand

2 x (3 x - 4) : 6 x^{2} - 8 x

6 x^{2} - 12 = 6 x^{2} - 8 x

Move

12

to the right side

6 x^{2} = 6 x^{2} - 8 x + 12

Subtract

6 x^{2} - 8 x

from both sides

6 x^{2} - (6 x^{2} - 8 x) = 6 x^{2} - 8 x + 12 - (6 x^{2} - 8 x)

Simplify

8 x = 12

Divide both sides by

8

x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = \frac{4}{3}

Combine undefined points with solutions:

x = \frac{3}{2}

\frac{- 8 x}{( x ^{2} - 4 ) ^{2}} = 0

\frac{5 x - 1}{1 - 2 x} = - 6

\frac{1}{x} = \frac{3}{6}

\frac{5}{6} = \frac{5 x}{x + 60}

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

What is the answer to ((6x^2-12))/((3x-4))=2x ?
The answer to ((6x^2-12))/((3x-4))=2x is x= 3/2
Solve for x: ((6x^2-12))/((3x-4))=2x
The solution is x= 3/2