Solve f(x)=x^2/4+4/x+1

$$f ( x ) = \frac { x ^ { 2 } } { 4 } + \frac { 4 } { x } + 1$$

Evaluate

$$\frac{x^{2}}{4}+1+\frac{4}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{x^{2}}{4} times \frac{x}{x}. Multiply \frac{4}{x} times \frac{4}{4}.

$$\frac{x^{2}x}{4x}+\frac{4\times 4}{4x}+1$$

Since \frac{x^{2}x}{4x} and \frac{4\times 4}{4x} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}x+4\times 4}{4x}+1$$

Do the multiplications in x^{2}x+4\times 4.

$$\frac{x^{3}+16}{4x}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4x}{4x}.

$$\frac{x^{3}+16}{4x}+\frac{4x}{4x}$$

Since \frac{x^{3}+16}{4x} and \frac{4x}{4x} have the same denominator, add them by adding their numerators.

$$\frac{x^{3}+16+4x}{4x}$$

Factor

$$\frac{\left(x+2\right)\left(x^{2}-2x+8\right)}{4x}$$