Solve a/x^2-4=-2/x+2

$$\frac { a } { x ^ { 2 } - 4 } = - \frac { 2 } { x + 2 }$$

Solve for a (complex solution)

$$a=4-2x$$

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

Solution Steps

Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x^{2}-4,x+2.

$$a=-\left(x-2\right)\times 2$$

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

$$a=-\left(2x-4\right)$$

To find the opposite of 2x-4, find the opposite of each term.

$$a=-2x+4$$

Solve for x (complex solution)

$$x=-\frac{a}{2}+2$$

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

Steps for Solving Linear Equation

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

$$a=-\left(x-2\right)\times 2$$

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

$$a=-\left(2x-4\right)$$

To find the opposite of 2x-4, find the opposite of each term.

$$a=-2x+4$$

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

$$-2x+4=a$$

Subtract 4 from both sides.

$$-2x=a-4$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{a-4}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{a-4}{-2}$$

Divide a-4 by -2.

$$x=-\frac{a}{2}+2$$

Variable x cannot be equal to any of the values -2,2.

$$x=-\frac{a}{2}+2\text{, }x\neq -2\text{ and }x\neq 2$$

Solve for a

$$a=4-2x$$

$$|x|\neq 2$$

Solution Steps

Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x^{2}-4,x+2.

$$a=-\left(x-2\right)\times 2$$

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

$$a=-\left(2x-4\right)$$

To find the opposite of 2x-4, find the opposite of each term.

$$a=-2x+4$$

Solve for x

$$x=-\frac{a}{2}+2$$

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

Steps for Solving Linear Equation

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

$$a=-\left(x-2\right)\times 2$$

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

$$a=-\left(2x-4\right)$$

To find the opposite of 2x-4, find the opposite of each term.

$$a=-2x+4$$

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

$$-2x+4=a$$

Subtract 4 from both sides.

$$-2x=a-4$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{a-4}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{a-4}{-2}$$

Divide a-4 by -2.

$$x=-\frac{a}{2}+2$$

Variable x cannot be equal to any of the values -2,2.

$$x=-\frac{a}{2}+2\text{, }x\neq -2\text{ and }x\neq 2$$