Solve 4c/c+1-4/c-1=4c^2+76/c^2-1

$$\frac { 4 c } { c + 1 } - \frac { 4 } { c - 1 } = \frac { 4 c ^ { 2 } + 76 } { c ^ { 2 } - 1 }$$

Solve for c

$$c=-10$$

Steps for Solving Linear Equation

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

$$\left(c-1\right)\times 4c-\left(c+1\right)\times 4=4c^{2}+76$$

Use the distributive property to multiply c-1 by 4.

$$\left(4c-4\right)c-\left(c+1\right)\times 4=4c^{2}+76$$

Use the distributive property to multiply 4c-4 by c.

$$4c^{2}-4c-\left(c+1\right)\times 4=4c^{2}+76$$

Use the distributive property to multiply c+1 by 4.

$$4c^{2}-4c-\left(4c+4\right)=4c^{2}+76$$

To find the opposite of 4c+4, find the opposite of each term.

$$4c^{2}-4c-4c-4=4c^{2}+76$$

Combine -4c and -4c to get -8c.

$$4c^{2}-8c-4=4c^{2}+76$$

Subtract 4c^{2} from both sides.

$$4c^{2}-8c-4-4c^{2}=76$$

Combine 4c^{2} and -4c^{2} to get 0.

$$-8c-4=76$$

Add 4 to both sides.

$$-8c=76+4$$

Add 76 and 4 to get 80.

$$-8c=80$$

Divide both sides by -8.

$$c=\frac{80}{-8}$$

Divide 80 by -8 to get -10.

$$c=-10$$