Solve -1/x^2-49-15/49-x^2

$$\frac { - 1 } { x ^ { 2 } - 49 } - \frac { 15 } { 49 - x ^ { 2 } }$$

Evaluate

$$\frac{14}{x^{2}-49}$$

Short Solution Steps

Factor x^{2}-49. Factor 49-x^{2}.

$$\frac{-1}{\left(x-7\right)\left(x+7\right)}-\frac{15}{\left(x-7\right)\left(-x-7\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-7\right)\left(x+7\right) and \left(x-7\right)\left(-x-7\right) is \left(x-7\right)\left(x+7\right). Multiply \frac{15}{\left(x-7\right)\left(-x-7\right)} times \frac{-1}{-1}.

$$\frac{-1}{\left(x-7\right)\left(x+7\right)}-\frac{15\left(-1\right)}{\left(x-7\right)\left(x+7\right)}$$

Since \frac{-1}{\left(x-7\right)\left(x+7\right)} and \frac{15\left(-1\right)}{\left(x-7\right)\left(x+7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-15\left(-1\right)}{\left(x-7\right)\left(x+7\right)}$$

Do the multiplications in -1-15\left(-1\right).

$$\frac{-1+15}{\left(x-7\right)\left(x+7\right)}$$

Do the calculations in -1+15.

$$\frac{14}{\left(x-7\right)\left(x+7\right)}$$

Expand \left(x-7\right)\left(x+7\right).

$$\frac{14}{x^{2}-49}$$

Differentiate w.r.t. x

$$-\frac{28x}{\left(x^{2}-49\right)^{2}}$$