Solve 2-x/x+2=4/5

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

Solve for x

$$x=\frac{2}{9}\approx 0.222222222$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 5\left(x+2\right), the least common multiple of x+2,5.

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

Use the distributive property to multiply 5 by 2-x.

$$10-5x=4\left(x+2\right)$$

Use the distributive property to multiply 4 by x+2.

$$10-5x=4x+8$$

Subtract 4x from both sides.

$$10-5x-4x=8$$

Combine -5x and -4x to get -9x.

$$10-9x=8$$

Subtract 10 from both sides.

$$-9x=8-10$$

Subtract 10 from 8 to get -2.

$$-9x=-2$$

Divide both sides by -9.

$$x=\frac{-2}{-9}$$

Fraction \frac{-2}{-9} can be simplified to \frac{2}{9} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{2}{9}$$