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

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

Solve for x

$$x=-\frac{5}{26}\approx -0.192307692$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{5},\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-1\right)\left(5x+2\right), the least common multiple of 5x+2,5x-1.

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

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

$$10x^{2}-7x+1=\left(5x+2\right)\left(2x+3\right)$$

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

$$10x^{2}-7x+1=10x^{2}+19x+6$$

Subtract 10x^{2} from both sides.

$$10x^{2}-7x+1-10x^{2}=19x+6$$

Combine 10x^{2} and -10x^{2} to get 0.

$$-7x+1=19x+6$$

Subtract 19x from both sides.

$$-7x+1-19x=6$$

Combine -7x and -19x to get -26x.

$$-26x+1=6$$

Subtract 1 from both sides.

$$-26x=6-1$$

Subtract 1 from 6 to get 5.

$$-26x=5$$

Divide both sides by -26.

$$x=\frac{5}{-26}$$

Fraction \frac{5}{-26} can be rewritten as -\frac{5}{26} by extracting the negative sign.

$$x=-\frac{5}{26}$$