Solve d(d+1)/3d-2*2-3d/(1+d)(d+4

$$\frac { d ( d + 1 ) } { 3 d - 2 } \times \frac { 2 - 3 d } { ( 1 + d ) ( d + 4 }$$

Evaluate

$$-\frac{d}{d+4}$$

Short Solution Steps

Use the distributive property to multiply d by d+1.

$$\frac{d^{2}+d}{3d-2}\times \frac{2-3d}{\left(1+d\right)\left(d+4\right)}$$

Apply the distributive property by multiplying each term of 1+d by each term of d+4.

$$\frac{d^{2}+d}{3d-2}\times \frac{2-3d}{d+4+d^{2}+4d}$$

Combine d and 4d to get 5d.

$$\frac{d^{2}+d}{3d-2}\times \frac{2-3d}{5d+4+d^{2}}$$

Multiply \frac{d^{2}+d}{3d-2} times \frac{2-3d}{5d+4+d^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(d^{2}+d\right)\left(2-3d\right)}{\left(3d-2\right)\left(5d+4+d^{2}\right)}$$

Extract the negative sign in 2-3d.

$$\frac{-\left(3d-2\right)\left(d^{2}+d\right)}{\left(3d-2\right)\left(d^{2}+5d+4\right)}$$

Cancel out 3d-2 in both numerator and denominator.

$$\frac{-\left(d^{2}+d\right)}{d^{2}+5d+4}$$

Factor the expressions that are not already factored.

$$\frac{-d\left(d+1\right)}{\left(d+1\right)\left(d+4\right)}$$

Cancel out d+1 in both numerator and denominator.

$$\frac{-d}{d+4}$$

Expand

$$-\frac{d}{d+4}$$

Short Solution Steps

Use the distributive property to multiply d by d+1.

$$\frac{d^{2}+d}{3d-2}\times \frac{2-3d}{\left(1+d\right)\left(d+4\right)}$$

Apply the distributive property by multiplying each term of 1+d by each term of d+4.

$$\frac{d^{2}+d}{3d-2}\times \frac{2-3d}{d+4+d^{2}+4d}$$

Combine d and 4d to get 5d.

$$\frac{d^{2}+d}{3d-2}\times \frac{2-3d}{5d+4+d^{2}}$$

Multiply \frac{d^{2}+d}{3d-2} times \frac{2-3d}{5d+4+d^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(d^{2}+d\right)\left(2-3d\right)}{\left(3d-2\right)\left(5d+4+d^{2}\right)}$$

Extract the negative sign in 2-3d.

$$\frac{-\left(3d-2\right)\left(d^{2}+d\right)}{\left(3d-2\right)\left(d^{2}+5d+4\right)}$$

Cancel out 3d-2 in both numerator and denominator.

$$\frac{-\left(d^{2}+d\right)}{d^{2}+5d+4}$$

Factor the expressions that are not already factored.

$$\frac{-d\left(d+1\right)}{\left(d+1\right)\left(d+4\right)}$$

Cancel out d+1 in both numerator and denominator.

$$\frac{-d}{d+4}$$