Solve 5/4-x=6x+4/16-x^2+4/4+x

$$\frac{ 5 }{ 4-x } = \frac{ 6x+4 }{ 16- { x }^{ 2 } } + \frac{ 4 }{ 4+x }$$

Solve for x

$$x=0$$

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 4-x,16-x^{2},4+x.

$$-\left(4+x\right)\times 5=-\left(6x+4\right)+\left(x-4\right)\times 4$$

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

$$\left(-4-x\right)\times 5=-\left(6x+4\right)+\left(x-4\right)\times 4$$

Use the distributive property to multiply -4-x by 5.

$$-20-5x=-\left(6x+4\right)+\left(x-4\right)\times 4$$

To find the opposite of 6x+4, find the opposite of each term.

$$-20-5x=-6x-4+\left(x-4\right)\times 4$$

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

$$-20-5x=-6x-4+4x-16$$

Combine -6x and 4x to get -2x.

$$-20-5x=-2x-4-16$$

Subtract 16 from -4 to get -20.

$$-20-5x=-2x-20$$

Add 2x to both sides.

$$-20-5x+2x=-20$$

Combine -5x and 2x to get -3x.

$$-20-3x=-20$$

Add 20 to both sides.

$$-3x=-20+20$$

Add -20 and 20 to get 0.

$$-3x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -3 is not equal to 0, x must be equal to 0.

$$x=0$$