Solve 2/3-6x^2/9x^2-1=2/3x-1

$$\frac { 2 } { 3 } - \frac { 6 x ^ { 2 } } { 9 x ^ { 2 } - 1 } = \frac { 2 } { 3 x - 1 }$$

Solve for x

$$x=-\frac{4}{9}\approx -0.444444444$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{1}{3},\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3\left(3x-1\right)\left(3x+1\right), the least common multiple of 3,9x^{2}-1,3x-1.

$$3\left(3x-1\right)\left(3x+1\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Use the distributive property to multiply 3 by 3x-1.

$$\left(9x-3\right)\left(3x+1\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Use the distributive property to multiply 9x-3 by 3x+1 and combine like terms.

$$\left(27x^{2}-3\right)\times \frac{2}{3}-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Use the distributive property to multiply 27x^{2}-3 by \frac{2}{3}.

$$18x^{2}-2-3\times 6x^{2}=\left(9x+3\right)\times 2$$

Multiply -3 and 6 to get -18.

$$18x^{2}-2-18x^{2}=\left(9x+3\right)\times 2$$

Combine 18x^{2} and -18x^{2} to get 0.

$$-2=\left(9x+3\right)\times 2$$

Use the distributive property to multiply 9x+3 by 2.

$$-2=18x+6$$

Swap sides so that all variable terms are on the left hand side.

$$18x+6=-2$$

Subtract 6 from both sides.

$$18x=-2-6$$

Subtract 6 from -2 to get -8.

$$18x=-8$$

Divide both sides by 18.

$$x=\frac{-8}{18}$$

Reduce the fraction \frac{-8}{18} to lowest terms by extracting and canceling out 2.

$$x=-\frac{4}{9}$$