# How do you simplify (r+6)/(6+r)?

Apr 1, 2018

$\frac{r + 6}{6 + r} = 1$

#### Explanation:

$r + 6 = 6 + r$, and trivially you have $\frac{r + 6}{6 + r} = 1$

Apr 1, 2018

$1$

#### Explanation:

Think about it: $r + 6 = 6 + r$

Therefore, the numerator and the denominator can cancel each other out to have a total value of $1$.

Apr 1, 2018

See explanation.

#### Explanation:

Since rhe result of addition does not depend on the order of operands we can write that:

## $r + 6 = 6 + r$

Knowing that we can write that:

## $\frac{r + 6}{6 + r} = \frac{r + 6}{r + 6} = 1$ 

The above equality is true for all $x$ for which the value is defined, i.e. for all real values other than $r = - 6$.

Apr 1, 2018

$1$

#### Explanation:

We have the same thing on the numerator and the same thing on the denominator, thus this expression is equal to $1$.

$r + 6$ is the same as $6 + r$, because addition is commutative. Thus, we would have:

$\frac{r + 6}{r + 6}$

The terms would cancel with each other, and we would essentially be left with a $1$. We can view this as the coefficient on the $r$ term.

In general, $\frac{a}{a} = 1$. So if the top and bottom of a fraction is the same, it is equal to $1$.

Hope this helps!