Solve x^2/4p-p/x-2p-x^2/4p-p/x+2p

$$\frac { \frac { x ^ { 2 } } { 4 p } - p } { x - 2 p } - \frac { \frac { x ^ { 2 } } { 4 p } - p } { x + 2 p }$$

Evaluate

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Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{4p}{4p}.

$$\frac{\frac{x^{2}}{4p}-\frac{p\times 4p}{4p}}{x-2p}-\frac{\frac{x^{2}}{4p}-p}{x+2p}$$

Since \frac{x^{2}}{4p} and \frac{p\times 4p}{4p} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-p\times 4p}{4p}}{x-2p}-\frac{\frac{x^{2}}{4p}-p}{x+2p}$$

Do the multiplications in x^{2}-p\times 4p.

$$\frac{\frac{x^{2}-4p^{2}}{4p}}{x-2p}-\frac{\frac{x^{2}}{4p}-p}{x+2p}$$

Express \frac{\frac{x^{2}-4p^{2}}{4p}}{x-2p} as a single fraction.

$$\frac{x^{2}-4p^{2}}{4p\left(x-2p\right)}-\frac{\frac{x^{2}}{4p}-p}{x+2p}$$

Factor the expressions that are not already factored in \frac{x^{2}-4p^{2}}{4p\left(x-2p\right)}.

$$\frac{\left(x-2p\right)\left(x+2p\right)}{4p\left(x-2p\right)}-\frac{\frac{x^{2}}{4p}-p}{x+2p}$$

Cancel out x-2p in both numerator and denominator.

$$\frac{x+2p}{4p}-\frac{\frac{x^{2}}{4p}-p}{x+2p}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{4p}{4p}.

$$\frac{x+2p}{4p}-\frac{\frac{x^{2}}{4p}-\frac{p\times 4p}{4p}}{x+2p}$$

Since \frac{x^{2}}{4p} and \frac{p\times 4p}{4p} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2p}{4p}-\frac{\frac{x^{2}-p\times 4p}{4p}}{x+2p}$$

Do the multiplications in x^{2}-p\times 4p.

$$\frac{x+2p}{4p}-\frac{\frac{x^{2}-4p^{2}}{4p}}{x+2p}$$

Express \frac{\frac{x^{2}-4p^{2}}{4p}}{x+2p} as a single fraction.

$$\frac{x+2p}{4p}-\frac{x^{2}-4p^{2}}{4p\left(x+2p\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}-4p^{2}}{4p\left(x+2p\right)}.

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

Cancel out x+2p in both numerator and denominator.

$$\frac{x+2p}{4p}-\frac{x-2p}{4p}$$

Since \frac{x+2p}{4p} and \frac{x-2p}{4p} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x+2p-\left(x-2p\right).

$$\frac{x+2p-x+2p}{4p}$$

Combine like terms in x+2p-x+2p.

$$\frac{4p}{4p}$$

Cancel out 4p in both numerator and denominator.

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Factor

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