Solve 1-25/x^2/frac{7{x}+35/x^2}

$$\frac { 1 - \frac { 25 } { x ^ { 2 } } } { \frac { 7 } { x } + \frac { 35 } { x ^ { 2 } } }$$

Evaluate

$$\frac{x-5}{7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{x^{2}}{x^{2}}-\frac{25}{x^{2}}}{\frac{7}{x}+\frac{35}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-25}{x^{2}}}{\frac{7}{x}+\frac{35}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{7}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}-25}{x^{2}}}{\frac{7x}{x^{2}}+\frac{35}{x^{2}}}$$

Since \frac{7x}{x^{2}} and \frac{35}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-25}{x^{2}}}{\frac{7x+35}{x^{2}}}$$

Divide \frac{x^{2}-25}{x^{2}} by \frac{7x+35}{x^{2}} by multiplying \frac{x^{2}-25}{x^{2}} by the reciprocal of \frac{7x+35}{x^{2}}.

$$\frac{\left(x^{2}-25\right)x^{2}}{x^{2}\left(7x+35\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}-25}{7x+35}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x+5\right)}{7\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-5}{7}$$

Expand

$$\frac{x-5}{7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{x^{2}}{x^{2}}-\frac{25}{x^{2}}}{\frac{7}{x}+\frac{35}{x^{2}}}$$

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

$$\frac{\frac{x^{2}-25}{x^{2}}}{\frac{7}{x}+\frac{35}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{7}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}-25}{x^{2}}}{\frac{7x}{x^{2}}+\frac{35}{x^{2}}}$$

Since \frac{7x}{x^{2}} and \frac{35}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-25}{x^{2}}}{\frac{7x+35}{x^{2}}}$$

Divide \frac{x^{2}-25}{x^{2}} by \frac{7x+35}{x^{2}} by multiplying \frac{x^{2}-25}{x^{2}} by the reciprocal of \frac{7x+35}{x^{2}}.

$$\frac{\left(x^{2}-25\right)x^{2}}{x^{2}\left(7x+35\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}-25}{7x+35}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x+5\right)}{7\left(x+5\right)}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-5}{7}$$