Solve fx=x+1/3(x+2)^3

$$f x = \frac { x + 1 } { 3 ( x + 2 ) ^ { 3 } }$$

Solve for f

$$f=\frac{x+1}{3x\left(x+2\right)^{3}}$$

$$x\neq -2\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(x+2\right)^{3}.

$$fx\times 3\left(x+2\right)^{3}=x+1$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$fx\times 3\left(x^{3}+6x^{2}+12x+8\right)=x+1$$

Use the distributive property to multiply fx\times 3 by x^{3}+6x^{2}+12x+8.

$$3fx^{4}+18fx^{3}+36fx^{2}+8fx\times 3=x+1$$

Multiply 8 and 3 to get 24.

$$3fx^{4}+18fx^{3}+36fx^{2}+24fx=x+1$$

Combine all terms containing f.

$$\left(3x^{4}+18x^{3}+36x^{2}+24x\right)f=x+1$$

Divide both sides by 3x^{4}+18x^{3}+36x^{2}+24x.

$$\frac{\left(3x^{4}+18x^{3}+36x^{2}+24x\right)f}{3x^{4}+18x^{3}+36x^{2}+24x}=\frac{x+1}{3x^{4}+18x^{3}+36x^{2}+24x}$$

Dividing by 3x^{4}+18x^{3}+36x^{2}+24x undoes the multiplication by 3x^{4}+18x^{3}+36x^{2}+24x.

$$f=\frac{x+1}{3x^{4}+18x^{3}+36x^{2}+24x}$$

Divide x+1 by 3x^{4}+18x^{3}+36x^{2}+24x.

$$f=\frac{x+1}{3x\left(x+2\right)^{3}}$$