Solve 4/x=20/6/frac{20{6}+x}

$$\frac{ 4 }{ x } = \frac{ \frac{ 20 }{ 6 } }{ \frac{ 20 }{ 6 } +x }$$

Solve for x

$$x=-20$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$4=3x\left(10+3x\right)^{-1}\times \frac{20}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$4=3x\left(10+3x\right)^{-1}\times \frac{10}{3}$$

Multiply 3 and \frac{10}{3} to get 10.

$$4=10x\left(10+3x\right)^{-1}$$

Swap sides so that all variable terms are on the left hand side.

$$10x\left(10+3x\right)^{-1}=4$$

Reorder the terms.

$$10\times \frac{1}{3x+10}x=4$$

Variable x cannot be equal to -\frac{10}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+10.

$$10\times 1x=4\left(3x+10\right)$$

Multiply 10 and 1 to get 10.

$$10x=4\left(3x+10\right)$$

Use the distributive property to multiply 4 by 3x+10.

$$10x=12x+40$$

Subtract 12x from both sides.

$$10x-12x=40$$

Combine 10x and -12x to get -2x.

$$-2x=40$$

Divide both sides by -2.

$$x=\frac{40}{-2}$$

Divide 40 by -2 to get -20.

$$x=-20$$