Solve x/1+3x-3-x/1-3x=0x/9x^2-1

$$\frac { x } { 1 + 3 x } - \frac { 3 - x } { 1 - 3 x } = \frac { 0 x } { 9 x ^ { 2 } - 1 }$$

Solve for x

$$x=-\frac{3}{7}\approx -0.428571429$$

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 \left(3x-1\right)\left(3x+1\right), the least common multiple of 1+3x,1-3x,9x^{2}-1.

$$\left(3x-1\right)x-\left(-1-3x\right)\left(3-x\right)=0x$$

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

$$3x^{2}-x-\left(-1-3x\right)\left(3-x\right)=0x$$

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

$$3x^{2}-x-\left(-3-8x+3x^{2}\right)=0x$$

To find the opposite of -3-8x+3x^{2}, find the opposite of each term.

$$3x^{2}-x+3+8x-3x^{2}=0x$$

Combine -x and 8x to get 7x.

$$3x^{2}+7x+3-3x^{2}=0x$$

Combine 3x^{2} and -3x^{2} to get 0.

$$7x+3=0x$$

Anything times zero gives zero.

$$7x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$7x=-3$$

Divide both sides by 7.

$$x=\frac{-3}{7}$$

Fraction \frac{-3}{7} can be rewritten as -\frac{3}{7} by extracting the negative sign.

$$x=-\frac{3}{7}$$