Solve b/b^2-121-6/b^2-11b

$$\frac { b } { b ^ { 2 } - 121 } - \frac { 6 } { b ^ { 2 } - 11 b }$$

Evaluate

$$\frac{b^{2}-6b-66}{b\left(b^{2}-121\right)}$$

Short Solution Steps

Factor b^{2}-121. Factor b^{2}-11b.

$$\frac{b}{\left(b-11\right)\left(b+11\right)}-\frac{6}{b\left(b-11\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b-11\right)\left(b+11\right) and b\left(b-11\right) is b\left(b-11\right)\left(b+11\right). Multiply \frac{b}{\left(b-11\right)\left(b+11\right)} times \frac{b}{b}. Multiply \frac{6}{b\left(b-11\right)} times \frac{b+11}{b+11}.

$$\frac{bb}{b\left(b-11\right)\left(b+11\right)}-\frac{6\left(b+11\right)}{b\left(b-11\right)\left(b+11\right)}$$

Since \frac{bb}{b\left(b-11\right)\left(b+11\right)} and \frac{6\left(b+11\right)}{b\left(b-11\right)\left(b+11\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{bb-6\left(b+11\right)}{b\left(b-11\right)\left(b+11\right)}$$

Do the multiplications in bb-6\left(b+11\right).

$$\frac{b^{2}-6b-66}{b\left(b-11\right)\left(b+11\right)}$$

Expand b\left(b-11\right)\left(b+11\right).

$$\frac{b^{2}-6b-66}{b^{3}-121b}$$

Differentiate w.r.t. b

$$\frac{-b^{4}+12b^{3}+77b^{2}-7986}{\left(b\left(b^{2}-121\right)\right)^{2}}$$