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

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Answer 1 · 2018-04-01T19:13:53

#(r+6)/(6+r)=1#

addition is commutative, so :
#r+6=6+r#, and trivially you have #(r+6)/(6+r)=1#

Answer 2 · 2018-04-01T19:14:31

#1#

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#.

Answer 3 · 2018-04-01T19:16:43

See 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:

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

Answer 4 · 2018-04-01T19:34:33

#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, #a/a=1#. So if the top and bottom of a fraction is the same, it is equal to #1#.

Hope this helps!