Solve 5/q+3-3/q-3=3q-1/q^2-9

$$\frac { 5 } { q + 3 } - \frac { 3 } { q - 3 } = \frac { 3 q - 1 } { q ^ { 2 } - 9 }$$

Solve for q

$$q=-23$$

Steps for Solving Linear Equation

Variable q 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(q-3\right)\left(q+3\right), the least common multiple of q+3,q-3,q^{2}-9.

$$\left(q-3\right)\times 5-\left(q+3\right)\times 3=3q-1$$

Use the distributive property to multiply q-3 by 5.

$$5q-15-\left(q+3\right)\times 3=3q-1$$

Use the distributive property to multiply q+3 by 3.

$$5q-15-\left(3q+9\right)=3q-1$$

To find the opposite of 3q+9, find the opposite of each term.

$$5q-15-3q-9=3q-1$$

Combine 5q and -3q to get 2q.

$$2q-15-9=3q-1$$

Subtract 9 from -15 to get -24.

$$2q-24=3q-1$$

Subtract 3q from both sides.

$$2q-24-3q=-1$$

Combine 2q and -3q to get -q.

$$-q-24=-1$$

Add 24 to both sides.

$$-q=-1+24$$

Add -1 and 24 to get 23.

$$-q=23$$

Multiply both sides by -1.

$$q=-23$$