Solve 2/a-1+3/a+1=7a/a^2-1-2/a

$$\frac{ 2 }{ a-1 } + \frac{ 3 }{ a+1 } = \frac{ 7a }{ { a }^{ 2 } -1 } - \frac{ 2 }{ a }$$

Solve for a

$$a=-2$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values -1,0,1 since division by zero is not defined. Multiply both sides of the equation by a\left(a-1\right)\left(a+1\right), the least common multiple of a-1,a+1,a^{2}-1,a.

$$a\left(a+1\right)\times 2+a\left(a-1\right)\times 3=a\times 7a-\left(a^{2}-1\right)\times 2$$

Use the distributive property to multiply a by a+1.

$$\left(a^{2}+a\right)\times 2+a\left(a-1\right)\times 3=a\times 7a-\left(a^{2}-1\right)\times 2$$

Use the distributive property to multiply a^{2}+a by 2.

$$2a^{2}+2a+a\left(a-1\right)\times 3=a\times 7a-\left(a^{2}-1\right)\times 2$$

Use the distributive property to multiply a by a-1.

$$2a^{2}+2a+\left(a^{2}-a\right)\times 3=a\times 7a-\left(a^{2}-1\right)\times 2$$

Use the distributive property to multiply a^{2}-a by 3.

$$2a^{2}+2a+3a^{2}-3a=a\times 7a-\left(a^{2}-1\right)\times 2$$

Combine 2a^{2} and 3a^{2} to get 5a^{2}.

$$5a^{2}+2a-3a=a\times 7a-\left(a^{2}-1\right)\times 2$$

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

$$5a^{2}-a=a\times 7a-\left(a^{2}-1\right)\times 2$$

Multiply a and a to get a^{2}.

$$5a^{2}-a=a^{2}\times 7-\left(a^{2}-1\right)\times 2$$

Use the distributive property to multiply a^{2}-1 by 2.

$$5a^{2}-a=a^{2}\times 7-\left(2a^{2}-2\right)$$

To find the opposite of 2a^{2}-2, find the opposite of each term.

$$5a^{2}-a=a^{2}\times 7-2a^{2}+2$$

Combine a^{2}\times 7 and -2a^{2} to get 5a^{2}.

$$5a^{2}-a=5a^{2}+2$$

Subtract 5a^{2} from both sides.

$$5a^{2}-a-5a^{2}=2$$

Combine 5a^{2} and -5a^{2} to get 0.

$$-a=2$$

Multiply both sides by -1.

$$a=-2$$