Solve 1/x^2+7-3x-1

$$\frac { 1 } { x ^ { 2 } + 7 } - 3 x - 1$$

Evaluate

$$-\frac{3x^{3}+x^{2}+21x+6}{x^{2}+7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -3x-1 times \frac{x^{2}+7}{x^{2}+7}.

$$\frac{1}{x^{2}+7}+\frac{\left(-3x-1\right)\left(x^{2}+7\right)}{x^{2}+7}$$

Since \frac{1}{x^{2}+7} and \frac{\left(-3x-1\right)\left(x^{2}+7\right)}{x^{2}+7} have the same denominator, add them by adding their numerators.

$$\frac{1+\left(-3x-1\right)\left(x^{2}+7\right)}{x^{2}+7}$$

Do the multiplications in 1+\left(-3x-1\right)\left(x^{2}+7\right).

$$\frac{1-3x^{3}-21x-x^{2}-7}{x^{2}+7}$$

Combine like terms in 1-3x^{3}-21x-x^{2}-7.

$$\frac{-6-3x^{3}-21x-x^{2}}{x^{2}+7}$$

Differentiate w.r.t. x

$$-\frac{3x^{4}+42x^{2}+2x+147}{\left(x^{2}+7\right)^{2}}$$