Solve a-6/a^2-4+a+1/a+2=a^2-2a-24/a^2-4

$$\frac { a - 6 } { a ^ { 2 } - 4 } + \frac { a + 1 } { a + 2 } = \frac { a ^ { 2 } - 2 a - 24 } { a ^ { 2 } - 4 }$$

Solve for a

$$a=-8$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(a-2\right)\left(a+2\right), the least common multiple of a^{2}-4,a+2.

$$a-6+\left(a-2\right)\left(a+1\right)=a^{2}-2a-24$$

Use the distributive property to multiply a-2 by a+1 and combine like terms.

$$a-6+a^{2}-a-2=a^{2}-2a-24$$

Combine a and -a to get 0.

$$-6+a^{2}-2=a^{2}-2a-24$$

Subtract 2 from -6 to get -8.

$$-8+a^{2}=a^{2}-2a-24$$

Subtract a^{2} from both sides.

$$-8+a^{2}-a^{2}=-2a-24$$

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

$$-8=-2a-24$$

Swap sides so that all variable terms are on the left hand side.

$$-2a-24=-8$$

Add 24 to both sides.

$$-2a=-8+24$$

Add -8 and 24 to get 16.

$$-2a=16$$

Divide both sides by -2.

$$a=\frac{16}{-2}$$

Divide 16 by -2 to get -8.

$$a=-8$$