Solve 1/x^2-5x^2+5/x-4=

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Since \frac{1-5x^{3}-5x}{x^{2}} and \frac{4x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

Since \frac{1-5x^{3}-5x}{x^{2}} and \frac{4x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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