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

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

Solve for x

$$x=-\frac{3}{5}=-0.6$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x-1 by x.

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

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

$$x^{2}-x=x^{2}+2x-3+\left(x+3\right)\times 2$$

Use the distributive property to multiply x+3 by 2.

$$x^{2}-x=x^{2}+2x-3+2x+6$$

Combine 2x and 2x to get 4x.

$$x^{2}-x=x^{2}+4x-3+6$$

Add -3 and 6 to get 3.

$$x^{2}-x=x^{2}+4x+3$$

Subtract x^{2} from both sides.

$$x^{2}-x-x^{2}=4x+3$$

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

$$-x=4x+3$$

Subtract 4x from both sides.

$$-x-4x=3$$

Combine -x and -4x to get -5x.

$$-5x=3$$

Divide both sides by -5.

$$x=\frac{3}{-5}$$

Fraction \frac{3}{-5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$x=-\frac{3}{5}$$