Solve 2x+8/4x^2-8x-5/2x=1/x

$$\frac { 2 x + 8 } { 4 x ^ { 2 } - 8 x } - \frac { 5 } { 2 x } = \frac { 1 } { x }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by 4x\left(x-2\right), the least common multiple of 4x^{2}-8x,2x,x.

$$2x+8-\left(2x-4\right)\times 5=4x-8$$

Use the distributive property to multiply 2x-4 by 5.

$$2x+8-\left(10x-20\right)=4x-8$$

To find the opposite of 10x-20, find the opposite of each term.

$$2x+8-10x+20=4x-8$$

Combine 2x and -10x to get -8x.

$$-8x+8+20=4x-8$$

Add 8 and 20 to get 28.

$$-8x+28=4x-8$$

Subtract 4x from both sides.

$$-8x+28-4x=-8$$

Combine -8x and -4x to get -12x.

$$-12x+28=-8$$

Subtract 28 from both sides.

$$-12x=-8-28$$

Subtract 28 from -8 to get -36.

$$-12x=-36$$

Divide both sides by -12.

$$x=\frac{-36}{-12}$$

Divide -36 by -12 to get 3.

$$x=3$$