How do you simplify #(2/a)/(1/(a+6))#?

1 Answer
Feb 27, 2017

Answer:

#(2/a)/(1/(a+6)) = 2+12/a#

with exclusion #a != -6#

Explanation:

Note that division is the same as multiplication by the reciprocal:

#(2/a)/(1/(a+6)) = (2/a)-:(1/(a+6))#

#color(white)((2/a)/(1/(a+6))) = (2/a)*((a+6)/1)#

#color(white)((2/a)/(1/(a+6))) = (2a+12)/a#

#color(white)((2/a)/(1/(a+6))) = 2+12/a#

Note that both the original expression and the simplified expression are undefined when #a=0#, since they both involve division by #0#.

By way of contrast, the original expression is undefined when #a=-6#, but the simplified expression is well defined.

So the original expression and simplified expression are not equivalent when #a=-6#. So we need to explicitly exclude the value #a=-6#.