Solve 1/x^2-1/p^2/x-p

$$\frac { \frac { 1 } { x ^ { 2 } } - \frac { 1 } { p ^ { 2 } } } { x - p }$$

Evaluate

$$-\frac{x+p}{\left(px\right)^{2}}$$

Short Solution Steps

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

$$\frac{\frac{p^{2}}{p^{2}x^{2}}-\frac{x^{2}}{p^{2}x^{2}}}{x-p}$$

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

$$\frac{\frac{p^{2}-x^{2}}{p^{2}x^{2}}}{x-p}$$

Express \frac{\frac{p^{2}-x^{2}}{p^{2}x^{2}}}{x-p} as a single fraction.

$$\frac{p^{2}-x^{2}}{p^{2}x^{2}\left(x-p\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in p-x.

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

Cancel out x-p in both numerator and denominator.

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

Expand the expression.

$$\frac{-x-p}{\left(px\right)^{2}}$$

Expand \left(px\right)^{2}.

$$\frac{-x-p}{p^{2}x^{2}}$$

Expand

$$-\frac{x+p}{\left(px\right)^{2}}$$

Short Solution Steps

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

$$\frac{\frac{p^{2}}{p^{2}x^{2}}-\frac{x^{2}}{p^{2}x^{2}}}{x-p}$$

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

$$\frac{\frac{p^{2}-x^{2}}{p^{2}x^{2}}}{x-p}$$

Express \frac{\frac{p^{2}-x^{2}}{p^{2}x^{2}}}{x-p} as a single fraction.

$$\frac{p^{2}-x^{2}}{p^{2}x^{2}\left(x-p\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in p-x.

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

Cancel out x-p in both numerator and denominator.

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

Expand the expression.

$$\frac{-x-p}{\left(px\right)^{2}}$$

Expand \left(px\right)^{2}.

$$\frac{-x-p}{p^{2}x^{2}}$$