Solve 2/x^2-8x+12-1/x-2=1/6x-36

$$\frac { 2 } { x ^ { 2 } - 8 x + 12 } - \frac { 1 } { x - 2 } = \frac { 1 } { 6 x - 36 }$$

Solve for x

$$x = \frac{50}{7} = 7\frac{1}{7} \approx 7.142857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,6 since division by zero is not defined. Multiply both sides of the equation by 6\left(x-6\right)\left(x-2\right), the least common multiple of x^{2}-8x+12,x-2,6x-36.

$$6\times 2-\left(6x-36\right)=x-2$$

Multiply 6 and 2 to get 12.

$$12-\left(6x-36\right)=x-2$$

To find the opposite of 6x-36, find the opposite of each term.

$$12-6x+36=x-2$$

Add 12 and 36 to get 48.

$$48-6x=x-2$$

Subtract x from both sides.

$$48-6x-x=-2$$

Combine -6x and -x to get -7x.

$$48-7x=-2$$

Subtract 48 from both sides.

$$-7x=-2-48$$

Subtract 48 from -2 to get -50.

$$-7x=-50$$

Divide both sides by -7.

$$x=\frac{-50}{-7}$$

Fraction \frac{-50}{-7} can be simplified to \frac{50}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{50}{7}$$