Solve f_{1}=2/3-2/3x+1

$$f _ { 1 } = \frac { 2 } { 3 } - \frac { 2 } { 3 x + 1 }$$

Solve for x

$$x=-\frac{3f_{1}+4}{3\left(3f_{1}-2\right)}$$

$$f_{1}\neq \frac{2}{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3\left(3x+1\right), the least common multiple of 3,3x+1.

$$f_{1}\times 3\left(3x+1\right)=3\left(3x+1\right)\times \frac{2}{3}-3\times 2$$

Use the distributive property to multiply f_{1}\times 3 by 3x+1.

$$9xf_{1}+f_{1}\times 3=3\left(3x+1\right)\times \frac{2}{3}-3\times 2$$

Multiply 3 and \frac{2}{3} to get 2.

$$9xf_{1}+f_{1}\times 3=2\left(3x+1\right)-3\times 2$$

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

$$9xf_{1}+f_{1}\times 3=6x+2-3\times 2$$

Multiply -3 and 2 to get -6.

$$9xf_{1}+f_{1}\times 3=6x+2-6$$

Subtract 6 from 2 to get -4.

$$9xf_{1}+f_{1}\times 3=6x-4$$

Subtract 6x from both sides.

$$9xf_{1}+f_{1}\times 3-6x=-4$$

Subtract f_{1}\times 3 from both sides.

$$9xf_{1}-6x=-4-f_{1}\times 3$$

Multiply -1 and 3 to get -3.

$$9xf_{1}-6x=-4-3f_{1}$$

Combine all terms containing x.

$$\left(9f_{1}-6\right)x=-4-3f_{1}$$

The equation is in standard form.

$$\left(9f_{1}-6\right)x=-3f_{1}-4$$

Divide both sides by -6+9f_{1}.

$$\frac{\left(9f_{1}-6\right)x}{9f_{1}-6}=\frac{-3f_{1}-4}{9f_{1}-6}$$

Dividing by -6+9f_{1} undoes the multiplication by -6+9f_{1}.

$$x=\frac{-3f_{1}-4}{9f_{1}-6}$$

Divide -4-3f_{1} by -6+9f_{1}.

$$x=-\frac{3f_{1}+4}{3\left(3f_{1}-2\right)}$$

Variable x cannot be equal to -\frac{1}{3}.

$$x=-\frac{3f_{1}+4}{3\left(3f_{1}-2\right)}\text{, }x\neq -\frac{1}{3}$$

Solve for f_1

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

$$x\neq -\frac{1}{3}$$