Solve 1/4p+q-1/4p-q=

$$\frac { 1 } { 4 p + q } - \frac { 1 } { 4 p - q } =$$

Evaluate

$$-\frac{2q}{16p^{2}-q^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4p+q and 4p-q is \left(4p+q\right)\left(4p-q\right). Multiply \frac{1}{4p+q} times \frac{4p-q}{4p-q}. Multiply \frac{1}{4p-q} times \frac{4p+q}{4p+q}.

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

Since \frac{4p-q}{\left(4p+q\right)\left(4p-q\right)} and \frac{4p+q}{\left(4p+q\right)\left(4p-q\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4p-q-\left(4p+q\right).

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

Combine like terms in 4p-q-4p-q.

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

Expand \left(4p+q\right)\left(4p-q\right).

$$\frac{-2q}{16p^{2}-q^{2}}$$

Differentiate w.r.t. q

$$\frac{2\left(-16p^{2}-q^{2}\right)}{\left(16p^{2}-q^{2}\right)^{2}}$$