Solve f(x)=1/x-1/x^2/frac{2{x^3}-3/x^4}

$$f ( x ) = \frac { \frac { 1 } { x } - \frac { 1 } { x ^ { 2 } } } { \frac { 2 } { x ^ { 3 } } - \frac { 3 } { x ^ { 4 } } }$$

Evaluate

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

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}.

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

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

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

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{2}{x^{3}} times \frac{x}{x}.

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

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

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

Divide \frac{x-1}{x^{2}} by \frac{2x-3}{x^{4}} by multiplying \frac{x-1}{x^{2}} by the reciprocal of \frac{2x-3}{x^{4}}.

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

Cancel out x^{2} in both numerator and denominator.

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

Use the distributive property to multiply x-1 by x^{2}.

$$\frac{x^{3}-x^{2}}{2x-3}$$

Expand

$$\frac{x^{3}-x^{2}}{2x-3}$$

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}.

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

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

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

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{2}{x^{3}} times \frac{x}{x}.

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

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

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

Divide \frac{x-1}{x^{2}} by \frac{2x-3}{x^{4}} by multiplying \frac{x-1}{x^{2}} by the reciprocal of \frac{2x-3}{x^{4}}.

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

Cancel out x^{2} in both numerator and denominator.

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

Use the distributive property to multiply x-1 by x^{2}.

$$\frac{x^{3}-x^{2}}{2x-3}$$