Solve (a+2)*(a-2)/a+3=a^2-4/a+3

$$\frac { ( a + 2 ) \cdot ( a - 2 ) } { a + 3 } = \frac { a ^ { 2 } - 4 } { a + 3 }$$

Solve for a

$$a\neq -3$$

Solution Steps

Variable a cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by a+3.

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

Consider \left(a+2\right)\left(a-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$a^{2}-4=a^{2}-4$$

Subtract a^{2} from both sides.

$$a^{2}-4-a^{2}=-4$$

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

$$-4=-4$$

Compare -4 and -4.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Variable a cannot be equal to -3.

$$a\in \mathrm{R}\setminus -3$$