Solve 9/j^2-1-7j/j^2-4j+3=-7/j-1

$$\frac { 9 } { j ^ { 2 } - 1 } - \frac { 7 j } { j ^ { 2 } - 4 j + 3 } = - \frac { 7 } { j - 1 }$$

Solve for j

$$j=-4$$

Steps for Solving Linear Equation

Variable j cannot be equal to any of the values -1,1,3 since division by zero is not defined. Multiply both sides of the equation by \left(j-3\right)\left(j-1\right)\left(j+1\right), the least common multiple of j^{2}-1,j^{2}-4j+3,j-1.

$$\left(j-3\right)\times 9-\left(j+1\right)\times 7j=-\left(j-3\right)\left(j+1\right)\times 7$$

Use the distributive property to multiply j-3 by 9.

$$9j-27-\left(j+1\right)\times 7j=-\left(j-3\right)\left(j+1\right)\times 7$$

Use the distributive property to multiply j+1 by 7.

$$9j-27-\left(7j+7\right)j=-\left(j-3\right)\left(j+1\right)\times 7$$

Use the distributive property to multiply 7j+7 by j.

$$9j-27-\left(7j^{2}+7j\right)=-\left(j-3\right)\left(j+1\right)\times 7$$

To find the opposite of 7j^{2}+7j, find the opposite of each term.

$$9j-27-7j^{2}-7j=-\left(j-3\right)\left(j+1\right)\times 7$$

Combine 9j and -7j to get 2j.

$$2j-27-7j^{2}=-\left(j-3\right)\left(j+1\right)\times 7$$

Use the distributive property to multiply j-3 by j+1 and combine like terms.

$$2j-27-7j^{2}=-\left(j^{2}-2j-3\right)\times 7$$

Use the distributive property to multiply j^{2}-2j-3 by 7.

$$2j-27-7j^{2}=-\left(7j^{2}-14j-21\right)$$

To find the opposite of 7j^{2}-14j-21, find the opposite of each term.

$$2j-27-7j^{2}=-7j^{2}+14j+21$$

Add 7j^{2} to both sides.

$$2j-27-7j^{2}+7j^{2}=14j+21$$

Combine -7j^{2} and 7j^{2} to get 0.

$$2j-27=14j+21$$

Subtract 14j from both sides.

$$2j-27-14j=21$$

Combine 2j and -14j to get -12j.

$$-12j-27=21$$

Add 27 to both sides.

$$-12j=21+27$$

Add 21 and 27 to get 48.

$$-12j=48$$

Divide both sides by -12.

$$j=\frac{48}{-12}$$

Divide 48 by -12 to get -4.

$$j=-4$$