Solve 1/4-x-3+x/x-4=1

$$\frac { 1 } { 4 - x } - \frac { 3 + x } { x - 4 } = 1$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4, the least common multiple of 4-x,x-4.

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

To find the opposite of 3+x, find the opposite of each term.

$$-1-3-x=x-4$$

Subtract 3 from -1 to get -4.

$$-4-x=x-4$$

Subtract x from both sides.

$$-4-x-x=-4$$

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

$$-4-2x=-4$$

Add 4 to both sides.

$$-2x=-4+4$$

Add -4 and 4 to get 0.

$$-2x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -2 is not equal to 0, x must be equal to 0.

$$x=0$$