Solve 1a/a^2-p^2-1/a-p

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

Evaluate

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

Short Solution Steps

Factor a^{2}-p^{2}.

$$\frac{1a}{\left(p+a\right)\left(-p+a\right)}-\frac{1}{a-p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(p+a\right)\left(-p+a\right) and a-p is \left(p+a\right)\left(-p+a\right). Multiply \frac{1}{a-p} times \frac{p+a}{p+a}.

$$\frac{1a}{\left(p+a\right)\left(-p+a\right)}-\frac{p+a}{\left(p+a\right)\left(-p+a\right)}$$

Since \frac{1a}{\left(p+a\right)\left(-p+a\right)} and \frac{p+a}{\left(p+a\right)\left(-p+a\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1a-\left(p+a\right)}{\left(p+a\right)\left(-p+a\right)}$$

Do the multiplications in 1a-\left(p+a\right).

$$\frac{a-p-a}{\left(p+a\right)\left(-p+a\right)}$$

Combine like terms in a-p-a.

$$\frac{-p}{\left(p+a\right)\left(-p+a\right)}$$

Expand \left(p+a\right)\left(-p+a\right).

$$\frac{-p}{-p^{2}+a^{2}}$$

Differentiate w.r.t. p

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