Solve 5x^2+3x/3x^2-15x/3x^-2

$$5 { x }^{ 2 } + \frac{ 3x }{ 3 { x }^{ 2 } } - \frac{ 15x }{ 3 { x }^{ -2 } }$$

Evaluate

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

Short Solution Steps

Cancel out 3x in both numerator and denominator.

$$5x^{2}+\frac{1}{x}-\frac{15x}{3x^{-2}}$$

Cancel out 3 in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x^{2}-5x^{3} times \frac{x}{x}.

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

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

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

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

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

Factor

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