Solve 1/x-3/x/2+frac{5{x}}

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

Evaluate

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

Solution Steps

Since \frac{1}{x} and \frac{3}{x} have the same denominator, subtract them by subtracting their numerators. Subtract 3 from 1 to get -2.

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

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

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

Since \frac{2x}{x} and \frac{5}{x} have the same denominator, add them by adding their numerators.

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

Divide \frac{-2}{x} by \frac{2x+5}{x} by multiplying \frac{-2}{x} by the reciprocal of \frac{2x+5}{x}.

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

Cancel out x in both numerator and denominator.

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

Expand

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

Solution Steps

Since \frac{1}{x} and \frac{3}{x} have the same denominator, subtract them by subtracting their numerators. Subtract 3 from 1 to get -2.

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

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

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

Since \frac{2x}{x} and \frac{5}{x} have the same denominator, add them by adding their numerators.

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

Divide \frac{-2}{x} by \frac{2x+5}{x} by multiplying \frac{-2}{x} by the reciprocal of \frac{2x+5}{x}.

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

Cancel out x in both numerator and denominator.

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