Solve by Factoring 1/(n-8)-1=7/(n-8)

Combine fractions with similar denominators.

Simplify the expression.

To write ${\displaystyle -1}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{n-8}{n-8}}$.

Simplify terms.

Simplify the numerator.

Move the negative in front of the fraction.

Subtract ${\displaystyle 7}$ from ${\displaystyle 1}$.

Move the negative in front of the fraction.

Combine ${\displaystyle -1}$ and ${\displaystyle \frac{n-8}{n-8}}$.

Combine the numerators over the common denominator.

Factor ${\displaystyle -1}$ out of ${\displaystyle -(n-8)-6}$.

Add ${\displaystyle -8}$ and ${\displaystyle 6}$.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number ${\displaystyle 1}$ is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of ${\displaystyle 1,1}$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

The factor for ${\displaystyle n-8}$ is ${\displaystyle n-8}$ itself.

${\displaystyle (n-8)}$ occurs ${\displaystyle 1}$ time.

The LCM of ${\displaystyle n-8}$ is the result of multiplying all factors the greatest number of times they occur in either term.

Multiply each term in ${\displaystyle -\frac{n-2}{n-8}=0}$ by ${\displaystyle n-8}$ in order to remove all the denominators from the equation.

Simplify ${\displaystyle -\frac{n-2}{n-8}\cdot (n-8)}$.

Multiply ${\displaystyle 0}$ by ${\displaystyle n-8}$.

Subtract ${\displaystyle 2}$ from both sides of the equation.

Multiply each term in ${\displaystyle -n=-2}$ by ${\displaystyle -1}$