Solve m/m+9=m-4/m+1

$$\frac { m } { m + 9 } = \frac { m - 4 } { m + 1 }$$

Solve for m

$$m=9$$

Steps for Solving Linear Equation

Variable m cannot be equal to any of the values -9,-1 since division by zero is not defined. Multiply both sides of the equation by \left(m+1\right)\left(m+9\right), the least common multiple of m+9,m+1.

$$\left(m+1\right)m=\left(m+9\right)\left(m-4\right)$$

Use the distributive property to multiply m+1 by m.

$$m^{2}+m=\left(m+9\right)\left(m-4\right)$$

Use the distributive property to multiply m+9 by m-4 and combine like terms.

$$m^{2}+m=m^{2}+5m-36$$

Subtract m^{2} from both sides.

$$m^{2}+m-m^{2}=5m-36$$

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

$$m=5m-36$$

Subtract 5m from both sides.

$$m-5m=-36$$

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

$$-4m=-36$$

Divide both sides by -4.

$$m=\frac{-36}{-4}$$

Divide -36 by -4 to get 9.

$$m=9$$