Solve d/d+3+5d+6/d^2+3d

$$\frac { d } { d + 3 } + \frac { 5 d + 6 } { d ^ { 2 } + 3 d }$$

Evaluate

$$\frac{d+2}{d}$$

Short Solution Steps

Factor d^{2}+3d.

$$\frac{d}{d+3}+\frac{5d+6}{d\left(d+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of d+3 and d\left(d+3\right) is d\left(d+3\right). Multiply \frac{d}{d+3} times \frac{d}{d}.

$$\frac{dd}{d\left(d+3\right)}+\frac{5d+6}{d\left(d+3\right)}$$

Since \frac{dd}{d\left(d+3\right)} and \frac{5d+6}{d\left(d+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{dd+5d+6}{d\left(d+3\right)}$$

Do the multiplications in dd+5d+6.

$$\frac{d^{2}+5d+6}{d\left(d+3\right)}$$

Factor the expressions that are not already factored in \frac{d^{2}+5d+6}{d\left(d+3\right)}.

$$\frac{\left(d+2\right)\left(d+3\right)}{d\left(d+3\right)}$$

Cancel out d+3 in both numerator and denominator.

$$\frac{d+2}{d}$$

Expand

$$\frac{d+2}{d}$$

Short Solution Steps

Factor d^{2}+3d.

$$\frac{d}{d+3}+\frac{5d+6}{d\left(d+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of d+3 and d\left(d+3\right) is d\left(d+3\right). Multiply \frac{d}{d+3} times \frac{d}{d}.

$$\frac{dd}{d\left(d+3\right)}+\frac{5d+6}{d\left(d+3\right)}$$

Since \frac{dd}{d\left(d+3\right)} and \frac{5d+6}{d\left(d+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{dd+5d+6}{d\left(d+3\right)}$$

Do the multiplications in dd+5d+6.

$$\frac{d^{2}+5d+6}{d\left(d+3\right)}$$

Factor the expressions that are not already factored in \frac{d^{2}+5d+6}{d\left(d+3\right)}.

$$\frac{\left(d+2\right)\left(d+3\right)}{d\left(d+3\right)}$$

Cancel out d+3 in both numerator and denominator.

$$\frac{d+2}{d}$$