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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

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

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

Multiply 2 and -\frac{3}{2} to get -3.

$$-2-3\left(3x-1\right)=2\times 2$$

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

$$-2-9x+3=2\times 2$$

Add -2 and 3 to get 1.

$$1-9x=2\times 2$$

Multiply 2 and 2 to get 4.

$$1-9x=4$$

Subtract 1 from both sides.

$$-9x=4-1$$

Subtract 1 from 4 to get 3.

$$-9x=3$$

Divide both sides by -9.

$$x=\frac{3}{-9}$$

Reduce the fraction \frac{3}{-9} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{3}$$