Solve 4+1/x/4-frac{1{x}}

$$\frac { 4 + \frac { 1 } { x } } { 4 - \frac { 1 } { x } }$$

Evaluate

$$\frac{4x+1}{4x-1}$$

Solution Steps

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

$$\frac{\frac{4x}{x}+\frac{1}{x}}{4-\frac{1}{x}}$$

Since \frac{4x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+1}{x}}{4-\frac{1}{x}}$$

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

$$\frac{\frac{4x+1}{x}}{\frac{4x}{x}-\frac{1}{x}}$$

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

$$\frac{\frac{4x+1}{x}}{\frac{4x-1}{x}}$$

Divide \frac{4x+1}{x} by \frac{4x-1}{x} by multiplying \frac{4x+1}{x} by the reciprocal of \frac{4x-1}{x}.

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

Cancel out x in both numerator and denominator.

$$\frac{4x+1}{4x-1}$$

Expand

$$\frac{4x+1}{4x-1}$$

Solution Steps

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

$$\frac{\frac{4x}{x}+\frac{1}{x}}{4-\frac{1}{x}}$$

Since \frac{4x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+1}{x}}{4-\frac{1}{x}}$$

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

$$\frac{\frac{4x+1}{x}}{\frac{4x}{x}-\frac{1}{x}}$$

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

$$\frac{\frac{4x+1}{x}}{\frac{4x-1}{x}}$$

Divide \frac{4x+1}{x} by \frac{4x-1}{x} by multiplying \frac{4x+1}{x} by the reciprocal of \frac{4x-1}{x}.

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

Cancel out x in both numerator and denominator.

$$\frac{4x+1}{4x-1}$$