Solve 2x-6/2x+5=3x+2/3x-1

$$\frac { 2 x - 6 } { 2 x + 5 } = \frac { 3 x + 2 } { 3 x - 1 }$$

Solve for x

$$x=-\frac{4}{39}\approx -0.102564103$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{2},\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-1\right)\left(2x+5\right), the least common multiple of 2x+5,3x-1.

$$\left(3x-1\right)\left(2x-6\right)=\left(2x+5\right)\left(3x+2\right)$$

Use the distributive property to multiply 3x-1 by 2x-6 and combine like terms.

$$6x^{2}-20x+6=\left(2x+5\right)\left(3x+2\right)$$

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

$$6x^{2}-20x+6=6x^{2}+19x+10$$

Subtract 6x^{2} from both sides.

$$6x^{2}-20x+6-6x^{2}=19x+10$$

Combine 6x^{2} and -6x^{2} to get 0.

$$-20x+6=19x+10$$

Subtract 19x from both sides.

$$-20x+6-19x=10$$

Combine -20x and -19x to get -39x.

$$-39x+6=10$$

Subtract 6 from both sides.

$$-39x=10-6$$

Subtract 6 from 10 to get 4.

$$-39x=4$$

Divide both sides by -39.

$$x=\frac{4}{-39}$$

Fraction \frac{4}{-39} can be rewritten as -\frac{4}{39} by extracting the negative sign.

$$x=-\frac{4}{39}$$