Solve a/a^2-9+3/a-3=1/a+3

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

Solve for a

$$a=-4$$

Steps for Solving Linear Equation

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

$$a+\left(a+3\right)\times 3=a-3$$

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

$$a+3a+9=a-3$$

Combine a and 3a to get 4a.

$$4a+9=a-3$$

Subtract a from both sides.

$$4a+9-a=-3$$

Combine 4a and -a to get 3a.

$$3a+9=-3$$

Subtract 9 from both sides.

$$3a=-3-9$$

Subtract 9 from -3 to get -12.

$$3a=-12$$

Divide both sides by 3.

$$a=\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$a=-4$$