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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

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

$$6x^{2}-19x+3=\left(2x+1\right)\left(3x-1\right)$$

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

$$6x^{2}-19x+3=6x^{2}+x-1$$

Subtract 6x^{2} from both sides.

$$6x^{2}-19x+3-6x^{2}=x-1$$

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

$$-19x+3=x-1$$

Subtract x from both sides.

$$-19x+3-x=-1$$

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

$$-20x+3=-1$$

Subtract 3 from both sides.

$$-20x=-1-3$$

Subtract 3 from -1 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.

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