Solve 5x-2/6x+1=5x+2/6x-1

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

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{1}{6},\frac{1}{6} since division by zero is not defined. Multiply both sides of the equation by \left(6x-1\right)\left(6x+1\right), the least common multiple of 6x+1,6x-1.

$$\left(6x-1\right)\left(5x-2\right)=\left(6x+1\right)\left(5x+2\right)$$

Use the distributive property to multiply 6x-1 by 5x-2 and combine like terms.

$$30x^{2}-17x+2=\left(6x+1\right)\left(5x+2\right)$$

Use the distributive property to multiply 6x+1 by 5x+2 and combine like terms.

$$30x^{2}-17x+2=30x^{2}+17x+2$$

Subtract 30x^{2} from both sides.

$$30x^{2}-17x+2-30x^{2}=17x+2$$

Combine 30x^{2} and -30x^{2} to get 0.

$$-17x+2=17x+2$$

Subtract 17x from both sides.

$$-17x+2-17x=2$$

Combine -17x and -17x to get -34x.

$$-34x+2=2$$

Subtract 2 from both sides.

$$-34x=2-2$$

Subtract 2 from 2 to get 0.

$$-34x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -34 is not equal to 0, x must be equal to 0.

$$x=0$$