Solve 1/x-4+m/x+4=m-3/x^2-16

$$\frac { 1 } { x - 4 } + \frac { m } { x + 4 } = \frac { m - 3 } { x ^ { 2 } - 16 }$$

Solve for m (complex solution)

$$m=-\frac{x+7}{x-5}$$

$$x\neq 5\text{ and }x\neq 4\text{ and }x\neq -4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-4\right)\left(x+4\right), the least common multiple of x-4,x+4,x^{2}-16.

$$x+4+\left(x-4\right)m=m-3$$

Use the distributive property to multiply x-4 by m.

$$x+4+xm-4m=m-3$$

Subtract m from both sides.

$$x+4+xm-4m-m=-3$$

Combine -4m and -m to get -5m.

$$x+4+xm-5m=-3$$

Subtract x from both sides.

$$4+xm-5m=-3-x$$

Subtract 4 from both sides.

$$xm-5m=-3-x-4$$

Subtract 4 from -3 to get -7.

$$xm-5m=-7-x$$

Combine all terms containing m.

$$\left(x-5\right)m=-7-x$$

The equation is in standard form.

$$\left(x-5\right)m=-x-7$$

Divide both sides by x-5.

$$\frac{\left(x-5\right)m}{x-5}=\frac{-x-7}{x-5}$$

Dividing by x-5 undoes the multiplication by x-5.

$$m=\frac{-x-7}{x-5}$$

Divide -7-x by x-5.

$$m=-\frac{x+7}{x-5}$$

Solve for m

$$m=-\frac{x+7}{x-5}$$

$$x\neq 5\text{ and }|x|\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-4\right)\left(x+4\right), the least common multiple of x-4,x+4,x^{2}-16.

$$x+4+\left(x-4\right)m=m-3$$

Use the distributive property to multiply x-4 by m.

$$x+4+xm-4m=m-3$$

Subtract m from both sides.

$$x+4+xm-4m-m=-3$$

Combine -4m and -m to get -5m.

$$x+4+xm-5m=-3$$

Subtract x from both sides.

$$4+xm-5m=-3-x$$

Subtract 4 from both sides.

$$xm-5m=-3-x-4$$

Subtract 4 from -3 to get -7.

$$xm-5m=-7-x$$

Combine all terms containing m.

$$\left(x-5\right)m=-7-x$$

The equation is in standard form.

$$\left(x-5\right)m=-x-7$$

Divide both sides by x-5.

$$\frac{\left(x-5\right)m}{x-5}=\frac{-x-7}{x-5}$$

Dividing by x-5 undoes the multiplication by x-5.

$$m=\frac{-x-7}{x-5}$$

Divide -7-x by x-5.

$$m=-\frac{x+7}{x-5}$$

Solve for x

$$x=-\frac{7-5m}{m+1}$$

$$m\neq 11\text{ and }m\neq -1\text{ and }m\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+4\right), the least common multiple of x-4,x+4,x^{2}-16.

$$x+4+\left(x-4\right)m=m-3$$

Use the distributive property to multiply x-4 by m.

$$x+4+xm-4m=m-3$$

Subtract 4 from both sides.

$$x+xm-4m=m-3-4$$

Subtract 4 from -3 to get -7.

$$x+xm-4m=m-7$$

Add 4m to both sides.

$$x+xm=m-7+4m$$

Combine m and 4m to get 5m.

$$x+xm=5m-7$$

Combine all terms containing x.

$$\left(1+m\right)x=5m-7$$

The equation is in standard form.

$$\left(m+1\right)x=5m-7$$

Divide both sides by 1+m.

$$\frac{\left(m+1\right)x}{m+1}=\frac{5m-7}{m+1}$$

Dividing by 1+m undoes the multiplication by 1+m.

$$x=\frac{5m-7}{m+1}$$

Variable x cannot be equal to any of the values -4,4.

$$x=\frac{5m-7}{m+1}\text{, }x\neq -4\text{ and }x\neq 4$$