Solve 1/x-1/3(frac{1{x})+5}

$$\frac{ \frac{ 1 }{ x } -1 }{ 3( \frac{ 1 }{ x } )+5 }$$

Evaluate

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

Express 3\times \frac{1}{x} as a single fraction.

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

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

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

Since \frac{3}{x} and \frac{5x}{x} have the same denominator, add them by adding their numerators.

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

Divide \frac{1-x}{x} by \frac{3+5x}{x} by multiplying \frac{1-x}{x} by the reciprocal of \frac{3+5x}{x}.

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

Cancel out x in both numerator and denominator.

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

Expand

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

Express 3\times \frac{1}{x} as a single fraction.

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

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

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

Since \frac{3}{x} and \frac{5x}{x} have the same denominator, add them by adding their numerators.

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

Divide \frac{1-x}{x} by \frac{3+5x}{x} by multiplying \frac{1-x}{x} by the reciprocal of \frac{3+5x}{x}.

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

Cancel out x in both numerator and denominator.

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