Solve 2/x^2-1/4x=9-x/2x^2X

$$\frac { 2 } { x ^ { 2 } } - \frac { 1 } { 4 x } = \frac { 9 - x } { 2 x ^ { 2 } } X$$

Solve for X

$$X=-\frac{x-8}{2\left(9-x\right)}$$

$$x\neq 9\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4x^{2}, the least common multiple of x^{2},4x,2x^{2}.

$$4\times 2-x=2\left(9-x\right)X$$

Multiply 4 and 2 to get 8.

$$8-x=2\left(9-x\right)X$$

Use the distributive property to multiply 2 by 9-x.

$$8-x=\left(18-2x\right)X$$

Use the distributive property to multiply 18-2x by X.

$$8-x=18X-2xX$$

Swap sides so that all variable terms are on the left hand side.

$$18X-2xX=8-x$$

Combine all terms containing X.

$$\left(18-2x\right)X=8-x$$

Divide both sides by 18-2x.

$$\frac{\left(18-2x\right)X}{18-2x}=\frac{8-x}{18-2x}$$

Dividing by 18-2x undoes the multiplication by 18-2x.

$$X=\frac{8-x}{18-2x}$$

Divide 8-x by 18-2x.

$$X=\frac{8-x}{2\left(9-x\right)}$$

Solve for x

$$x=-\frac{2\left(4-9X\right)}{2X-1}$$

$$X\neq \frac{4}{9}\text{ and }X\neq \frac{1}{2}$$