Solve m+6/m-1/m+2=m^2+8m+16/m^2+2m

$$\frac { m + 6 } { m } - \frac { 1 } { m + 2 } = \frac { m ^ { 2 } + 8 m + 16 } { m ^ { 2 } + 2 m }$$

Solve for m

$$m=-4$$

Steps for Solving Linear Equation

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

$$\left(m+2\right)\left(m+6\right)-m=m^{2}+8m+16$$

Use the distributive property to multiply m+2 by m+6 and combine like terms.

$$m^{2}+8m+12-m=m^{2}+8m+16$$

Subtract m^{2} from both sides.

$$m^{2}+8m+12-m-m^{2}=8m+16$$

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

$$8m+12-m=8m+16$$

Subtract 8m from both sides.

$$8m+12-m-8m=16$$

Combine 8m and -8m to get 0.

$$12-m=16$$

Subtract 12 from both sides.

$$-m=16-12$$

Subtract 12 from 16 to get 4.

$$-m=4$$

Multiply both sides by -1.

$$m=-4$$