Solve {c}{f(x)=x^3/x^2+x+1}{x=1}

$$\left. \begin{array} { c } { f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + x + 1 } } \\ { x = 1 } \end{array} \right.$$

Solve for f, x

$$x=1$$

$$f=\frac{1}{3}\approx 0.333333333$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$f\times 1=\frac{1^{3}}{1^{2}+1+1}$$

Calculate 1 to the power of 3 and get 1.

$$f\times 1=\frac{1}{1^{2}+1+1}$$

Calculate 1 to the power of 2 and get 1.

$$f\times 1=\frac{1}{1+1+1}$$

Add 1 and 1 to get 2.

$$f\times 1=\frac{1}{2+1}$$

Add 2 and 1 to get 3.

$$f\times 1=\frac{1}{3}$$

Divide both sides by 1.

$$f=\frac{\frac{1}{3}}{1}$$

Express \frac{\frac{1}{3}}{1} as a single fraction.

$$f=\frac{1}{3\times 1}$$

Cancel out 1 in both numerator and denominator.

$$f=\frac{1}{3}$$

The system is now solved.

$$f=\frac{1}{3} x=1$$