Solve 3x-1/5x+2=3x+1/5x-2

$$\frac { 3 x - 1 } { 5 x + 2 } = \frac { 3 x + 1 } { 5 x - 2 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{5},\frac{2}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-2\right)\left(5x+2\right), the least common multiple of 5x+2,5x-2.

$$\left(5x-2\right)\left(3x-1\right)=\left(5x+2\right)\left(3x+1\right)$$

Use the distributive property to multiply 5x-2 by 3x-1 and combine like terms.

$$15x^{2}-11x+2=\left(5x+2\right)\left(3x+1\right)$$

Use the distributive property to multiply 5x+2 by 3x+1 and combine like terms.

$$15x^{2}-11x+2=15x^{2}+11x+2$$

Subtract 15x^{2} from both sides.

$$15x^{2}-11x+2-15x^{2}=11x+2$$

Combine 15x^{2} and -15x^{2} to get 0.

$$-11x+2=11x+2$$

Subtract 11x from both sides.

$$-11x+2-11x=2$$

Combine -11x and -11x to get -22x.

$$-22x+2=2$$

Subtract 2 from both sides.

$$-22x=2-2$$

Subtract 2 from 2 to get 0.

$$-22x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -22 is not equal to 0, x must be equal to 0.

$$x=0$$