Solve x/25-1/x/1+frac{5{x}}

$$\frac { \frac { x } { 25 } - \frac { 1 } { x } } { 1 + \frac { 5 } { x } }$$

Evaluate

$$\frac{x-5}{25}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and x is 25x. Multiply \frac{x}{25} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{25}{25}.

$$\frac{\frac{xx}{25x}-\frac{25}{25x}}{1+\frac{5}{x}}$$

Since \frac{xx}{25x} and \frac{25}{25x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-25}{25x}}{1+\frac{5}{x}}$$

Do the multiplications in xx-25.

$$\frac{\frac{x^{2}-25}{25x}}{1+\frac{5}{x}}$$

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

$$\frac{\frac{x^{2}-25}{25x}}{\frac{x}{x}+\frac{5}{x}}$$

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

$$\frac{\frac{x^{2}-25}{25x}}{\frac{x+5}{x}}$$

Divide \frac{x^{2}-25}{25x} by \frac{x+5}{x} by multiplying \frac{x^{2}-25}{25x} by the reciprocal of \frac{x+5}{x}.

$$\frac{\left(x^{2}-25\right)x}{25x\left(x+5\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}-25}{25\left(x+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x+5\right)}{25\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-5}{25}$$

Expand

$$\frac{x}{25}-\frac{1}{5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and x is 25x. Multiply \frac{x}{25} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{25}{25}.

$$\frac{\frac{xx}{25x}-\frac{25}{25x}}{1+\frac{5}{x}}$$

Since \frac{xx}{25x} and \frac{25}{25x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-25}{25x}}{1+\frac{5}{x}}$$

Do the multiplications in xx-25.

$$\frac{\frac{x^{2}-25}{25x}}{1+\frac{5}{x}}$$

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

$$\frac{\frac{x^{2}-25}{25x}}{\frac{x}{x}+\frac{5}{x}}$$

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

$$\frac{\frac{x^{2}-25}{25x}}{\frac{x+5}{x}}$$

Divide \frac{x^{2}-25}{25x} by \frac{x+5}{x} by multiplying \frac{x^{2}-25}{25x} by the reciprocal of \frac{x+5}{x}.

$$\frac{\left(x^{2}-25\right)x}{25x\left(x+5\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}-25}{25\left(x+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x+5\right)}{25\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-5}{25}$$