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

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x-3 by 3.

$$x+1+\left(3x-9\right)x=3\left(x-3\right)\left(x+1\right)$$

Use the distributive property to multiply 3x-9 by x.

$$x+1+3x^{2}-9x=3\left(x-3\right)\left(x+1\right)$$

Combine x and -9x to get -8x.

$$-8x+1+3x^{2}=3\left(x-3\right)\left(x+1\right)$$

Use the distributive property to multiply 3 by x-3.

$$-8x+1+3x^{2}=\left(3x-9\right)\left(x+1\right)$$

Use the distributive property to multiply 3x-9 by x+1 and combine like terms.

$$-8x+1+3x^{2}=3x^{2}-6x-9$$

Subtract 3x^{2} from both sides.

$$-8x+1+3x^{2}-3x^{2}=-6x-9$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-8x+1=-6x-9$$

Add 6x to both sides.

$$-8x+1+6x=-9$$

Combine -8x and 6x to get -2x.

$$-2x+1=-9$$

Subtract 1 from both sides.

$$-2x=-9-1$$

Subtract 1 from -9 to get -10.

$$-2x=-10$$

Divide both sides by -2.

$$x=\frac{-10}{-2}$$

Divide -10 by -2 to get 5.

$$x=5$$