Solve 6-x/x+4=x/6-x

$$\frac{ 6-x }{ x+4 } = \frac{ x }{ 6-x }$$

Solve for x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(x+4\right), the least common multiple of x+4,6-x.

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

Use the distributive property to multiply x-6 by 6-x and combine like terms.

$$12x-x^{2}-36=-\left(4+x\right)x$$

Use the distributive property to multiply -1 by 4+x.

$$12x-x^{2}-36=\left(-4-x\right)x$$

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

$$12x-x^{2}-36=-4x-x^{2}$$

Add 4x to both sides.

$$12x-x^{2}-36+4x=-x^{2}$$

Combine 12x and 4x to get 16x.

$$16x-x^{2}-36=-x^{2}$$

Add x^{2} to both sides.

$$16x-x^{2}-36+x^{2}=0$$

Combine -x^{2} and x^{2} to get 0.

$$16x-36=0$$

Add 36 to both sides. Anything plus zero gives itself.

$$16x=36$$

Divide both sides by 16.

$$x=\frac{36}{16}$$

Reduce the fraction \frac{36}{16} to lowest terms by extracting and canceling out 4.

$$x=\frac{9}{4}$$