Solve 6.68E-20=[1/3+x]^2/(frac{1{3}+x)(2/3+x)}

$$6.68 E - 20 = \frac { [ \frac { 1 } { 3 } + x ] ^ { 2 } } { ( \frac { 1 } { 3 } + x ) ( \frac { 2 } { 3 } + x ) }$$

Solve for E

$$E=\frac{25\left(63x+41\right)}{167\left(3x+2\right)}$$

$$x\neq -\frac{1}{3}\text{ and }x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Cancel out x+\frac{1}{3} in both numerator and denominator.

$$6.68E-20=\frac{x+\frac{1}{3}}{x+\frac{2}{3}}$$

Factor the expressions that are not already factored in \frac{x+\frac{1}{3}}{x+\frac{2}{3}}.

$$6.68E-20=\frac{\frac{1}{3}\left(3x+1\right)}{\frac{1}{3}\left(3x+2\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$6.68E-20=\frac{3x+1}{\left(\frac{1}{3}\right)^{0}\left(3x+2\right)}$$

Calculate \frac{1}{3} to the power of 0 and get 1.

$$6.68E-20=\frac{3x+1}{1\left(3x+2\right)}$$

Use the distributive property to multiply 1 by 3x+2.

$$6.68E-20=\frac{3x+1}{3x+2}$$

Add 20 to both sides.

$$6.68E=\frac{3x+1}{3x+2}+20$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 20 times \frac{3x+2}{3x+2}.

$$6.68E=\frac{3x+1}{3x+2}+\frac{20\left(3x+2\right)}{3x+2}$$

Since \frac{3x+1}{3x+2} and \frac{20\left(3x+2\right)}{3x+2} have the same denominator, add them by adding their numerators.

$$6.68E=\frac{3x+1+20\left(3x+2\right)}{3x+2}$$

Do the multiplications in 3x+1+20\left(3x+2\right).

$$6.68E=\frac{3x+1+60x+40}{3x+2}$$

Combine like terms in 3x+1+60x+40.

$$6.68E=\frac{63x+41}{3x+2}$$

Multiply both sides of the equation by 3x+2.

$$6.68E\left(3x+2\right)=63x+41$$

Use the distributive property to multiply 6.68E by 3x+2.

$$20.04Ex+13.36E=63x+41$$

Combine all terms containing E.

$$\left(20.04x+13.36\right)E=63x+41$$

The equation is in standard form.

$$\frac{501x+334}{25}E=63x+41$$

Divide both sides by 20.04x+13.36.

$$\frac{25\times \frac{501x+334}{25}E}{501x+334}=\frac{25\left(63x+41\right)}{501x+334}$$

Dividing by 20.04x+13.36 undoes the multiplication by 20.04x+13.36.

$$E=\frac{25\left(63x+41\right)}{501x+334}$$

Solve for x

$$x=-\frac{334E-1025}{3\left(167E-525\right)}$$

$$E\neq \frac{500}{167}\text{ and }E\neq \frac{525}{167}$$