Solve 106/x^2-16+3x-1/4-x=2x-1/x+4-5

$$\frac { 106 } { x ^ { 2 } - 16 } + \frac { 3 x - 1 } { 4 - x } = \frac { 2 x - 1 } { x + 4 } - 5$$

Solve for x

$$x=13$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+4\right), the least common multiple of x^{2}-16,4-x,x+4.

$$106-\left(4+x\right)\left(3x-1\right)=\left(x-4\right)\left(2x-1\right)+\left(x-4\right)\left(x+4\right)\left(-5\right)$$

Use the distributive property to multiply -1 by 4+x.

$$106+\left(-4-x\right)\left(3x-1\right)=\left(x-4\right)\left(2x-1\right)+\left(x-4\right)\left(x+4\right)\left(-5\right)$$

Use the distributive property to multiply -4-x by 3x-1 and combine like terms.

$$106-11x+4-3x^{2}=\left(x-4\right)\left(2x-1\right)+\left(x-4\right)\left(x+4\right)\left(-5\right)$$

Add 106 and 4 to get 110.

$$110-11x-3x^{2}=\left(x-4\right)\left(2x-1\right)+\left(x-4\right)\left(x+4\right)\left(-5\right)$$

Use the distributive property to multiply x-4 by 2x-1 and combine like terms.

$$110-11x-3x^{2}=2x^{2}-9x+4+\left(x-4\right)\left(x+4\right)\left(-5\right)$$

Use the distributive property to multiply x-4 by x+4 and combine like terms.

$$110-11x-3x^{2}=2x^{2}-9x+4+\left(x^{2}-16\right)\left(-5\right)$$

Use the distributive property to multiply x^{2}-16 by -5.

$$110-11x-3x^{2}=2x^{2}-9x+4-5x^{2}+80$$

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$110-11x-3x^{2}=-3x^{2}-9x+4+80$$

Add 4 and 80 to get 84.

$$110-11x-3x^{2}=-3x^{2}-9x+84$$

Add 3x^{2} to both sides.

$$110-11x-3x^{2}+3x^{2}=-9x+84$$

Combine -3x^{2} and 3x^{2} to get 0.

$$110-11x=-9x+84$$

Add 9x to both sides.

$$110-11x+9x=84$$

Combine -11x and 9x to get -2x.

$$110-2x=84$$

Subtract 110 from both sides.

$$-2x=84-110$$

Subtract 110 from 84 to get -26.

$$-2x=-26$$

Divide both sides by -2.

$$x=\frac{-26}{-2}$$

Divide -26 by -2 to get 13.

$$x=13$$