Solve d^2+4d-21/d^2+10d+25*d^2-3d-40/2d^2-6d

$$\frac { d ^ { 2 } + 4 d - 21 } { d ^ { 2 } + 10 d + 25 } \times \frac { d ^ { 2 } - 3 d - 40 } { 2 d ^ { 2 } - 6 d }$$

Evaluate

$$\frac{\left(d-8\right)\left(d+7\right)}{2d\left(d+5\right)}$$

Short Solution Steps

Multiply \frac{d^{2}+4d-21}{d^{2}+10d+25} times \frac{d^{2}-3d-40}{2d^{2}-6d} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(d^{2}+4d-21\right)\left(d^{2}-3d-40\right)}{\left(d^{2}+10d+25\right)\left(2d^{2}-6d\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(d-8\right)\left(d-3\right)\left(d+5\right)\left(d+7\right)}{2d\left(d-3\right)\left(d+5\right)^{2}}$$

Cancel out \left(d-3\right)\left(d+5\right) in both numerator and denominator.

$$\frac{\left(d-8\right)\left(d+7\right)}{2d\left(d+5\right)}$$

Expand the expression.

$$\frac{d^{2}-d-56}{2d^{2}+10d}$$

Expand

$$\frac{d^{2}-d-56}{2d\left(d+5\right)}$$

Short Solution Steps

Multiply \frac{d^{2}+4d-21}{d^{2}+10d+25} times \frac{d^{2}-3d-40}{2d^{2}-6d} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(d^{2}+4d-21\right)\left(d^{2}-3d-40\right)}{\left(d^{2}+10d+25\right)\left(2d^{2}-6d\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(d-8\right)\left(d-3\right)\left(d+5\right)\left(d+7\right)}{2d\left(d-3\right)\left(d+5\right)^{2}}$$

Cancel out \left(d-3\right)\left(d+5\right) in both numerator and denominator.

$$\frac{\left(d-8\right)\left(d+7\right)}{2d\left(d+5\right)}$$

Expand the expression.

$$\frac{d^{2}-d-56}{2d^{2}+10d}$$