Solve 5/m-3-7/m+3=-2/m^2-9

$$\frac { 5 } { m - 3 } - \frac { 7 } { m + 3 } = \frac { - 2 } { m ^ { 2 } - 9 }$$

Solve for m

$$m=19$$

Steps for Solving Linear Equation

Variable m cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(m-3\right)\left(m+3\right), the least common multiple of m-3,m+3,m^{2}-9.

$$\left(m+3\right)\times 5-\left(m-3\right)\times 7=-2$$

Use the distributive property to multiply m+3 by 5.

$$5m+15-\left(m-3\right)\times 7=-2$$

Use the distributive property to multiply m-3 by 7.

$$5m+15-\left(7m-21\right)=-2$$

To find the opposite of 7m-21, find the opposite of each term.

$$5m+15-7m+21=-2$$

Combine 5m and -7m to get -2m.

$$-2m+15+21=-2$$

Add 15 and 21 to get 36.

$$-2m+36=-2$$

Subtract 36 from both sides.

$$-2m=-2-36$$

Subtract 36 from -2 to get -38.

$$-2m=-38$$

Divide both sides by -2.

$$m=\frac{-38}{-2}$$

Divide -38 by -2 to get 19.

$$m=19$$