Solve d/10d+7-(d-2)

$$\frac { d } { 10 d + 7 } - ( d - 2 )$$

Evaluate

$$\frac{2\left(7+7d-5d^{2}\right)}{10d+7}$$

Short Solution Steps

To find the opposite of d-2, find the opposite of each term.

$$\frac{d}{10d+7}-d-\left(-2\right)$$

The opposite of -2 is 2.

$$\frac{d}{10d+7}-d+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -d+2 times \frac{10d+7}{10d+7}.

$$\frac{d}{10d+7}+\frac{\left(-d+2\right)\left(10d+7\right)}{10d+7}$$

Since \frac{d}{10d+7} and \frac{\left(-d+2\right)\left(10d+7\right)}{10d+7} have the same denominator, add them by adding their numerators.

$$\frac{d+\left(-d+2\right)\left(10d+7\right)}{10d+7}$$

Do the multiplications in d+\left(-d+2\right)\left(10d+7\right).

$$\frac{d-10d^{2}-7d+20d+14}{10d+7}$$

Combine like terms in d-10d^{2}-7d+20d+14.

$$\frac{14d-10d^{2}+14}{10d+7}$$

Expand

$$-\frac{2\left(5d^{2}-7d-7\right)}{10d+7}$$

Short Solution Steps

To find the opposite of d-2, find the opposite of each term.

$$\frac{d}{10d+7}-d-\left(-2\right)$$

The opposite of -2 is 2.

$$\frac{d}{10d+7}-d+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -d+2 times \frac{10d+7}{10d+7}.

$$\frac{d}{10d+7}+\frac{\left(-d+2\right)\left(10d+7\right)}{10d+7}$$

Since \frac{d}{10d+7} and \frac{\left(-d+2\right)\left(10d+7\right)}{10d+7} have the same denominator, add them by adding their numerators.

$$\frac{d+\left(-d+2\right)\left(10d+7\right)}{10d+7}$$

Do the multiplications in d+\left(-d+2\right)\left(10d+7\right).

$$\frac{d-10d^{2}-7d+20d+14}{10d+7}$$

Combine like terms in d-10d^{2}-7d+20d+14.

$$\frac{14d-10d^{2}+14}{10d+7}$$