Solve 32/x^2-4x-1/x=3/x-4

$$\frac { 32 } { x ^ { 2 } - 4 x } - \frac { 1 } { x } = \frac { 3 } { x - 4 }$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,4 since division by zero is not defined. Multiply both sides of the equation by x\left(x-4\right), the least common multiple of x^{2}-4x,x,x-4.

$$32-\left(x-4\right)=x\times 3$$

To find the opposite of x-4, find the opposite of each term.

$$32-x+4=x\times 3$$

Add 32 and 4 to get 36.

$$36-x=x\times 3$$

Subtract x\times 3 from both sides.

$$36-x-x\times 3=0$$

Combine -x and -x\times 3 to get -4x.

$$36-4x=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$-4x=-36$$

Divide both sides by -4.

$$x=\frac{-36}{-4}$$

Divide -36 by -4 to get 9.

$$x=9$$