Solve 1/x+2=3/4-x

$$\frac{ 1 }{ x+2 } = \frac{ 3 }{ 4-x }$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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

$$x-4=-\left(2+x\right)\times 3$$

Multiply -1 and 3 to get -3.

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

Use the distributive property to multiply -3 by 2+x.

$$x-4=-6-3x$$

Add 3x to both sides.

$$x-4+3x=-6$$

Combine x and 3x to get 4x.

$$4x-4=-6$$

Add 4 to both sides.

$$4x=-6+4$$

Add -6 and 4 to get -2.

$$4x=-2$$

Divide both sides by 4.

$$x=\frac{-2}{4}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{2}$$