Solve (1/x+1/x^2)(4/x^3-6/x^4)quad

$$( \frac { 1 } { x } + \frac { 1 } { x ^ { 2 } } ) ( \frac { 4 } { x ^ { 3 } } - \frac { 6 } { x ^ { 4 } } ) \quad$$

Evaluate

$$\frac{2\left(2x-3\right)\left(x+1\right)}{x^{6}}$$

Short Solution Steps

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{1}{x} times \frac{x}{x}.

$$\left(\frac{x}{x^{2}}+\frac{1}{x^{2}}\right)\left(\frac{4}{x^{3}}-\frac{6}{x^{4}}\right)$$

Since \frac{x}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+1}{x^{2}}\left(\frac{4}{x^{3}}-\frac{6}{x^{4}}\right)$$

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

$$\frac{x+1}{x^{2}}\left(\frac{4x}{x^{4}}-\frac{6}{x^{4}}\right)$$

Since \frac{4x}{x^{4}} and \frac{6}{x^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+1}{x^{2}}\times \frac{4x-6}{x^{4}}$$

Multiply \frac{x+1}{x^{2}} times \frac{4x-6}{x^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+1\right)\left(4x-6\right)}{x^{2}x^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Use the distributive property to multiply x+1 by 4x-6 and combine like terms.

$$\frac{4x^{2}-2x-6}{x^{6}}$$

Expand

$$\frac{2\left(2x^{2}-x-3\right)}{x^{6}}$$

Short Solution Steps

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{1}{x} times \frac{x}{x}.

$$\left(\frac{x}{x^{2}}+\frac{1}{x^{2}}\right)\left(\frac{4}{x^{3}}-\frac{6}{x^{4}}\right)$$

Since \frac{x}{x^{2}} and \frac{1}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+1}{x^{2}}\left(\frac{4}{x^{3}}-\frac{6}{x^{4}}\right)$$

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

$$\frac{x+1}{x^{2}}\left(\frac{4x}{x^{4}}-\frac{6}{x^{4}}\right)$$

Since \frac{4x}{x^{4}} and \frac{6}{x^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+1}{x^{2}}\times \frac{4x-6}{x^{4}}$$

Multiply \frac{x+1}{x^{2}} times \frac{4x-6}{x^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+1\right)\left(4x-6\right)}{x^{2}x^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Use the distributive property to multiply x+1 by 4x-6 and combine like terms.

$$\frac{4x^{2}-2x-6}{x^{6}}$$