Solve 1/5+5/x/frac{1{25}-25/x^2}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x is 5x. Multiply \frac{1}{5} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{5}{5}.

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

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

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

Do the multiplications in x+5\times 5.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and x^{2} is 25x^{2}. Multiply \frac{1}{25} times \frac{x^{2}}{x^{2}}. Multiply \frac{25}{x^{2}} times \frac{25}{25}.

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

Since \frac{x^{2}}{25x^{2}} and \frac{25\times 25}{25x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-25\times 25.

$$\frac{\frac{x+25}{5x}}{\frac{x^{2}-625}{25x^{2}}}$$

Divide \frac{x+25}{5x} by \frac{x^{2}-625}{25x^{2}} by multiplying \frac{x+25}{5x} by the reciprocal of \frac{x^{2}-625}{25x^{2}}.

$$\frac{\left(x+25\right)\times 25x^{2}}{5x\left(x^{2}-625\right)}$$

Cancel out 5x in both numerator and denominator.

$$\frac{5x\left(x+25\right)}{x^{2}-625}$$

Factor the expressions that are not already factored.

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

Cancel out x+25 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x is 5x. Multiply \frac{1}{5} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{5}{5}.

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

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

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

Do the multiplications in x+5\times 5.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and x^{2} is 25x^{2}. Multiply \frac{1}{25} times \frac{x^{2}}{x^{2}}. Multiply \frac{25}{x^{2}} times \frac{25}{25}.

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

Since \frac{x^{2}}{25x^{2}} and \frac{25\times 25}{25x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-25\times 25.

$$\frac{\frac{x+25}{5x}}{\frac{x^{2}-625}{25x^{2}}}$$

Divide \frac{x+25}{5x} by \frac{x^{2}-625}{25x^{2}} by multiplying \frac{x+25}{5x} by the reciprocal of \frac{x^{2}-625}{25x^{2}}.

$$\frac{\left(x+25\right)\times 25x^{2}}{5x\left(x^{2}-625\right)}$$

Cancel out 5x in both numerator and denominator.

$$\frac{5x\left(x+25\right)}{x^{2}-625}$$

Factor the expressions that are not already factored.

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

Cancel out x+25 in both numerator and denominator.

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