How do you simplify and find the excluded value of #(m - 3 )/( 3 - m )#?

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Answer 1 · 2017-05-19T14:03:29

See a solution process below:

First, rewrite the numerator as:

#(-1(-m +3))/(3 - m) => (-1(3 - m))/(3 - m)#

Now, cancel like terms in the numerator and denominator to complete the simplification:

#(-1color(red)(cancel(color(black)((3 - m)))))/color(red)(cancel(color(black)(3 - m))) => -1#

Because we cannot divide by #0# the numerator, or, #3 - m# cannot equal #0#.

To find the excluded value set #3 - m# equal to #0# and solve for #m#:

#3 - m = 0#

#-color(red)(3) + 3 - m = -color(red)(3) + 0#

#0 - m = -3#

#-m = -3#

#color(red)(-1) xx -m = color(red)(-1) xx -3#

#m = 3#

The excluded value is #m = 3#