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

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

Solve for x

$$x=-\frac{1}{5}=-0.2$$

Steps for Solving Linear Equation

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

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

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

$$2x^{2}+9x+9=\left(2x-1\right)\left(x-5\right)$$

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

$$2x^{2}+9x+9=2x^{2}-11x+5$$

Subtract 2x^{2} from both sides.

$$2x^{2}+9x+9-2x^{2}=-11x+5$$

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

$$9x+9=-11x+5$$

Add 11x to both sides.

$$9x+9+11x=5$$

Combine 9x and 11x to get 20x.

$$20x+9=5$$

Subtract 9 from both sides.

$$20x=5-9$$

Subtract 9 from 5 to get -4.

$$20x=-4$$

Divide both sides by 20.

$$x=\frac{-4}{20}$$

Reduce the fraction \frac{-4}{20} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{5}$$