Solve 2k+(m-2)-2km/m^2-4-8=0

$$2 k + ( m - 2 ) \frac { - 2 k m } { m ^ { 2 } - 4 } - 8 = 0$$

Solve for k (complex solution)

$$k=2\left(m+2\right)$$

$$m\neq -2\text{ and }m\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(m-2\right)\left(m+2\right).

$$2k\left(m-2\right)\left(m+2\right)+\left(m-2\right)\left(-2\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply 2k by m-2.

$$\left(2km-4k\right)\left(m+2\right)+\left(m-2\right)\left(-2\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply 2km-4k by m+2 and combine like terms.

$$2km^{2}-8k+\left(m-2\right)\left(-2\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply m-2 by -2.

$$2km^{2}-8k+\left(-2m+4\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply -2m+4 by k.

$$2km^{2}-8k+\left(-2mk+4k\right)m+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply -2mk+4k by m.

$$2km^{2}-8k-2km^{2}+4km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Combine 2km^{2} and -2km^{2} to get 0.

$$-8k+4km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply m-2 by m+2 and combine like terms.

$$-8k+4km+\left(m^{2}-4\right)\left(-8\right)=0$$

Use the distributive property to multiply m^{2}-4 by -8.

$$-8k+4km-8m^{2}+32=0$$

Add 8m^{2} to both sides. Anything plus zero gives itself.

$$-8k+4km+32=8m^{2}$$

Subtract 32 from both sides.

$$-8k+4km=8m^{2}-32$$

Combine all terms containing k.

$$\left(-8+4m\right)k=8m^{2}-32$$

The equation is in standard form.

$$\left(4m-8\right)k=8m^{2}-32$$

Divide both sides by -8+4m.

$$\frac{\left(4m-8\right)k}{4m-8}=\frac{8m^{2}-32}{4m-8}$$

Dividing by -8+4m undoes the multiplication by -8+4m.

$$k=\frac{8m^{2}-32}{4m-8}$$

Divide 8m^{2}-32 by -8+4m.

$$k=2m+4$$

Solve for k

$$k=2\left(m+2\right)$$

$$|m|\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(m-2\right)\left(m+2\right).

$$2k\left(m-2\right)\left(m+2\right)+\left(m-2\right)\left(-2\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply 2k by m-2.

$$\left(2km-4k\right)\left(m+2\right)+\left(m-2\right)\left(-2\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply 2km-4k by m+2 and combine like terms.

$$2km^{2}-8k+\left(m-2\right)\left(-2\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply m-2 by -2.

$$2km^{2}-8k+\left(-2m+4\right)km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply -2m+4 by k.

$$2km^{2}-8k+\left(-2mk+4k\right)m+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply -2mk+4k by m.

$$2km^{2}-8k-2km^{2}+4km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Combine 2km^{2} and -2km^{2} to get 0.

$$-8k+4km+\left(m-2\right)\left(m+2\right)\left(-8\right)=0$$

Use the distributive property to multiply m-2 by m+2 and combine like terms.

$$-8k+4km+\left(m^{2}-4\right)\left(-8\right)=0$$

Use the distributive property to multiply m^{2}-4 by -8.

$$-8k+4km-8m^{2}+32=0$$

Add 8m^{2} to both sides. Anything plus zero gives itself.

$$-8k+4km+32=8m^{2}$$

Subtract 32 from both sides.

$$-8k+4km=8m^{2}-32$$

Combine all terms containing k.

$$\left(-8+4m\right)k=8m^{2}-32$$

The equation is in standard form.

$$\left(4m-8\right)k=8m^{2}-32$$

Divide both sides by -8+4m.

$$\frac{\left(4m-8\right)k}{4m-8}=\frac{8m^{2}-32}{4m-8}$$

Dividing by -8+4m undoes the multiplication by -8+4m.

$$k=\frac{8m^{2}-32}{4m-8}$$

Divide 8m^{2}-32 by -8+4m.

$$k=2m+4$$

Solve for m

$$m=\frac{k-4}{2}$$

$$k\neq 0\text{ and }k\neq 8$$