Solve n-1/10n+10-6/2

$$\frac { n - 1 } { 10 n + 10 } - \frac { 6 } { 2 }$$

Evaluate

$$-\frac{29n+31}{10\left(n+1\right)}$$

Short Solution Steps

Divide 6 by 2 to get 3.

$$\frac{n-1}{10n+10}-3$$

Factor 10n+10.

$$\frac{n-1}{10\left(n+1\right)}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{10\left(n+1\right)}{10\left(n+1\right)}.

$$\frac{n-1}{10\left(n+1\right)}-\frac{3\times 10\left(n+1\right)}{10\left(n+1\right)}$$

Since \frac{n-1}{10\left(n+1\right)} and \frac{3\times 10\left(n+1\right)}{10\left(n+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{n-1-3\times 10\left(n+1\right)}{10\left(n+1\right)}$$

Do the multiplications in n-1-3\times 10\left(n+1\right).

$$\frac{n-1-30n-30}{10\left(n+1\right)}$$

Combine like terms in n-1-30n-30.

$$\frac{-29n-31}{10\left(n+1\right)}$$

Expand 10\left(n+1\right).

$$\frac{-29n-31}{10n+10}$$

Expand

$$-\frac{29n+31}{10\left(n+1\right)}$$

Short Solution Steps

Divide 6 by 2 to get 3.

$$\frac{n-1}{10n+10}-3$$

Factor 10n+10.

$$\frac{n-1}{10\left(n+1\right)}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{10\left(n+1\right)}{10\left(n+1\right)}.

$$\frac{n-1}{10\left(n+1\right)}-\frac{3\times 10\left(n+1\right)}{10\left(n+1\right)}$$

Since \frac{n-1}{10\left(n+1\right)} and \frac{3\times 10\left(n+1\right)}{10\left(n+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{n-1-3\times 10\left(n+1\right)}{10\left(n+1\right)}$$

Do the multiplications in n-1-3\times 10\left(n+1\right).

$$\frac{n-1-30n-30}{10\left(n+1\right)}$$

Combine like terms in n-1-30n-30.

$$\frac{-29n-31}{10\left(n+1\right)}$$

Expand 10\left(n+1\right).

$$\frac{-29n-31}{10n+10}$$