Solve 3n(n+1)-(3n-2)(n+1)/n

$$\frac { 3 n ( n + 1 ) - ( 3 n - 2 ) ( n + 1 ) } { n }$$

Evaluate

$$2+\frac{2}{n}$$

Short Solution Steps

Use the distributive property to multiply 3n by n+1.

$$\frac{3n^{2}+3n-\left(3n-2\right)\left(n+1\right)}{n}$$

Apply the distributive property by multiplying each term of 3n-2 by each term of n+1.

$$\frac{3n^{2}+3n-\left(3n^{2}+3n-2n-2\right)}{n}$$

Combine 3n and -2n to get n.

$$\frac{3n^{2}+3n-\left(3n^{2}+n-2\right)}{n}$$

To find the opposite of 3n^{2}+n-2, find the opposite of each term.

$$\frac{3n^{2}+3n-3n^{2}-n-\left(-2\right)}{n}$$

The opposite of -2 is 2.

$$\frac{3n^{2}+3n-3n^{2}-n+2}{n}$$

Combine 3n^{2} and -3n^{2} to get 0.

$$\frac{3n-n+2}{n}$$

Combine 3n and -n to get 2n.

$$\frac{2n+2}{n}$$

Expand

$$2+\frac{2}{n}$$

Short Solution Steps

Use the distributive property to multiply 3n by n+1.

$$\frac{3n^{2}+3n-\left(3n-2\right)\left(n+1\right)}{n}$$

Apply the distributive property by multiplying each term of 3n-2 by each term of n+1.

$$\frac{3n^{2}+3n-\left(3n^{2}+3n-2n-2\right)}{n}$$

Combine 3n and -2n to get n.

$$\frac{3n^{2}+3n-\left(3n^{2}+n-2\right)}{n}$$

To find the opposite of 3n^{2}+n-2, find the opposite of each term.

$$\frac{3n^{2}+3n-3n^{2}-n-\left(-2\right)}{n}$$

The opposite of -2 is 2.

$$\frac{3n^{2}+3n-3n^{2}-n+2}{n}$$

Combine 3n^{2} and -3n^{2} to get 0.

$$\frac{3n-n+2}{n}$$

Combine 3n and -n to get 2n.

$$\frac{2n+2}{n}$$