Solve 5/r^2-10r+30-7

$$\frac { 5 } { r ^ { 2 } - 10 r + 30 } - 7$$

Evaluate

$$\frac{-7r^{2}+70r-205}{r^{2}-10r+30}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{r^{2}-10r+30}{r^{2}-10r+30}.

$$\frac{5}{r^{2}-10r+30}-\frac{7\left(r^{2}-10r+30\right)}{r^{2}-10r+30}$$

Since \frac{5}{r^{2}-10r+30} and \frac{7\left(r^{2}-10r+30\right)}{r^{2}-10r+30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-7\left(r^{2}-10r+30\right)}{r^{2}-10r+30}$$

Do the multiplications in 5-7\left(r^{2}-10r+30\right).

$$\frac{5-7r^{2}+70r-210}{r^{2}-10r+30}$$

Combine like terms in 5-7r^{2}+70r-210.

$$\frac{-205-7r^{2}+70r}{r^{2}-10r+30}$$

Differentiate w.r.t. r

$$\frac{10\left(5-r\right)}{\left(r^{2}-10r+30\right)^{2}}$$