Solve f(x)=3x^3-1/x^3+4x^-4

$$f ( x ) = 3 x ^ { 3 } - \frac { 1 } { x ^ { 3 } } + 4 x ^ { - 4 }$$

Evaluate

$$\frac{3x^{7}-x+4}{x^{4}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{3}+4x^{-4} times \frac{x^{3}}{x^{3}}.

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

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

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

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

$$\frac{3x^{6}+4\times \frac{1}{x}-1}{x^{3}}$$

Express 4\times \frac{1}{x} as a single fraction.

$$\frac{3x^{6}+\frac{4}{x}-1}{x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{6}-1 times \frac{x}{x}.

$$\frac{\frac{\left(3x^{6}-1\right)x}{x}+\frac{4}{x}}{x^{3}}$$

Since \frac{\left(3x^{6}-1\right)x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(3x^{6}-1\right)x+4}{x}}{x^{3}}$$

Do the multiplications in \left(3x^{6}-1\right)x+4.

$$\frac{\frac{3x^{7}-x+4}{x}}{x^{3}}$$

Express \frac{\frac{3x^{7}-x+4}{x}}{x^{3}} as a single fraction.

$$\frac{3x^{7}-x+4}{xx^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{3x^{7}-x+4}{x^{4}}$$

Factor

$$\frac{3x^{7}-x+4}{x^{4}}$$