Solve 2/3+x=10/3-x

$$\frac{ 2 }{ 3+x } = \frac{ 10 }{ 3-x }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right), the least common multiple of 3+x,3-x.

$$\left(x-3\right)\times 2=-\left(3+x\right)\times 10$$

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

$$2x-6=-\left(3+x\right)\times 10$$

Multiply -1 and 10 to get -10.

$$2x-6=-10\left(3+x\right)$$

Use the distributive property to multiply -10 by 3+x.

$$2x-6=-30-10x$$

Add 10x to both sides.

$$2x-6+10x=-30$$

Combine 2x and 10x to get 12x.

$$12x-6=-30$$

Add 6 to both sides.

$$12x=-30+6$$

Add -30 and 6 to get -24.

$$12x=-24$$

Divide both sides by 12.

$$x=\frac{-24}{12}$$

Divide -24 by 12 to get -2.

$$x=-2$$