Question

How do you simplify \[\dfrac{r+6}{6+r}\]?

Answer 1

Hint: For the given question we are given to solve the problem \[\dfrac{r+6}{6+r}\]. Now we have to solve the given fraction, as we can see that the numerator has \[r+6\] and the denominator has \[6+r\]. By observing the values of numerator and denominator we can have the results.

Complete step by step solution:
\[\dfrac{r+6}{6+r}\]
We all know that the answer is 1 because the terms on numerator and denominator is same so we can divide both of them so we will get the solution as 1
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:
\[r+6=r+6\]
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 \[\dfrac{a}{a}=1\]. So if the top and bottom of a fraction is the same, it is equal to 1.
And we can solve this problem in another way
Since the result of addition does not depend on the order of operands we can write that:
\[r+6=r+6\]
Knowing that we can write that:
\[\Rightarrow \dfrac{r+6}{r+6}=\dfrac{r+6}{r+6}=1\]
 The above equality is true for all x for which the value is defined, i.e. for all real values other than r=−6.

Note: We can do this problem only in these types because this is based under addition which is commutative law. The question will become difficult if the numerator and denominator are not the same. In that case we have to do partition for the fraction.