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

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

Solve for a

$$a = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

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,a^{2}-4,a+2.

$$a+2+6a=\left(a-2\right)\times 2$$

Combine a and 6a to get 7a.

$$7a+2=\left(a-2\right)\times 2$$

Use the distributive property to multiply a-2 by 2.

$$7a+2=2a-4$$

Subtract 2a from both sides.

$$7a+2-2a=-4$$

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

$$5a+2=-4$$

Subtract 2 from both sides.

$$5a=-4-2$$

Subtract 2 from -4 to get -6.

$$5a=-6$$

Divide both sides by 5.

$$a=\frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$a=-\frac{6}{5}$$