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

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

Evaluate

$$\frac{4x-1}{2\left(x+5\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in 2\times 2x-1.

$$\frac{\frac{4x-1}{2x}}{1+\frac{5}{x}}$$

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

$$\frac{\frac{4x-1}{2x}}{\frac{x}{x}+\frac{5}{x}}$$

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

$$\frac{\frac{4x-1}{2x}}{\frac{x+5}{x}}$$

Divide \frac{4x-1}{2x} by \frac{x+5}{x} by multiplying \frac{4x-1}{2x} by the reciprocal of \frac{x+5}{x}.

$$\frac{\left(4x-1\right)x}{2x\left(x+5\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4x-1}{2\left(x+5\right)}$$

Use the distributive property to multiply 2 by x+5.

$$\frac{4x-1}{2x+10}$$

Expand

$$\frac{4x-1}{2\left(x+5\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in 2\times 2x-1.

$$\frac{\frac{4x-1}{2x}}{1+\frac{5}{x}}$$

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

$$\frac{\frac{4x-1}{2x}}{\frac{x}{x}+\frac{5}{x}}$$

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

$$\frac{\frac{4x-1}{2x}}{\frac{x+5}{x}}$$

Divide \frac{4x-1}{2x} by \frac{x+5}{x} by multiplying \frac{4x-1}{2x} by the reciprocal of \frac{x+5}{x}.

$$\frac{\left(4x-1\right)x}{2x\left(x+5\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4x-1}{2\left(x+5\right)}$$

Use the distributive property to multiply 2 by x+5.

$$\frac{4x-1}{2x+10}$$