Solve f(x)=4x^2+5x-1/x+2/x^2

$$f ( x ) = 4 x ^ { 2 } + 5 x - \frac { 1 } { x } + \frac { 2 } { x ^ { 2 } }$$

Evaluate

$$4x^{2}+5x-\frac{1}{x}+\frac{2}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2}+5x times \frac{x}{x}.

$$\frac{\left(4x^{2}+5x\right)x}{x}-\frac{1}{x}+\frac{2}{x^{2}}$$

Since \frac{\left(4x^{2}+5x\right)x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(4x^{2}+5x\right)x-1}{x}+\frac{2}{x^{2}}$$

Do the multiplications in \left(4x^{2}+5x\right)x-1.

$$\frac{4x^{3}+5x^{2}-1}{x}+\frac{2}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{4x^{3}+5x^{2}-1}{x} times \frac{x}{x}.

$$\frac{\left(4x^{3}+5x^{2}-1\right)x}{x^{2}}+\frac{2}{x^{2}}$$

Since \frac{\left(4x^{3}+5x^{2}-1\right)x}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(4x^{3}+5x^{2}-1\right)x+2}{x^{2}}$$

Do the multiplications in \left(4x^{3}+5x^{2}-1\right)x+2.

$$\frac{4x^{4}+5x^{3}-x+2}{x^{2}}$$

Factor

$$\frac{4x^{4}+5x^{3}-x+2}{x^{2}}$$