Solve d^2-d/d^2-1divd+11/d^2+12d+11

$$\frac { d ^ { 2 } - d } { d ^ { 2 } - 1 } \div \frac { d + 11 } { d ^ { 2 } + 12 d + 11 }$$

Evaluate

$$d$$

Short Solution Steps

Divide \frac{d^{2}-d}{d^{2}-1} by \frac{d+11}{d^{2}+12d+11} by multiplying \frac{d^{2}-d}{d^{2}-1} by the reciprocal of \frac{d+11}{d^{2}+12d+11}.

$$\frac{\left(d^{2}-d\right)\left(d^{2}+12d+11\right)}{\left(d^{2}-1\right)\left(d+11\right)}$$

Factor the expressions that are not already factored.

$$\frac{d\left(d-1\right)\left(d+1\right)\left(d+11\right)}{\left(d-1\right)\left(d+1\right)\left(d+11\right)}$$

Cancel out \left(d-1\right)\left(d+1\right)\left(d+11\right) in both numerator and denominator.

$$d$$

Differentiate w.r.t. d

$$1$$

Steps Using Definition of a Derivative

Divide \frac{d^{2}-d}{d^{2}-1} by \frac{d+11}{d^{2}+12d+11} by multiplying \frac{d^{2}-d}{d^{2}-1} by the reciprocal of \frac{d+11}{d^{2}+12d+11}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{\left(d^{2}-d\right)\left(d^{2}+12d+11\right)}{\left(d^{2}-1\right)\left(d+11\right)})$$

Factor the expressions that are not already factored in \frac{\left(d^{2}-d\right)\left(d^{2}+12d+11\right)}{\left(d^{2}-1\right)\left(d+11\right)}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d\left(d-1\right)\left(d+1\right)\left(d+11\right)}{\left(d-1\right)\left(d+1\right)\left(d+11\right)})$$

Cancel out \left(d-1\right)\left(d+1\right)\left(d+11\right) in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d)$$

The derivative of ax^{n} is nax^{n-1}.

$$d^{1-1}$$

Subtract 1 from 1.

$$d^{0}$$

For any term t except 0, t^{0}=1.

$$1$$