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

Question

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

Eva Adamson · Accepted Answer

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#

Julia Adams · Answer

undefined To simplify and find the excluded value of (m - 3)/(3 - m), we can start by factoring out a negative from the denominator to make it (m - 3)/(-m + 3). Next, we can simplify the expression by canceling out the common factor of -1, resulting in -(m - 3)/(m - 3). Finally, we can simplify further by canceling out the common factor of (m - 3), leaving us with -1 as the simplified expression. The excluded value in this case is m = 3, as it would result in a division by zero.

Eva Adamson · Answer

undefined To simplify and find the excluded value of $ \frac{m - 3}{3 - m} $, follow these steps:

1. Factor out a negative from the denominator:
$$ \frac{m - 3}{-(m - 3)} $$

2. Cancel out the common factor $ m - 3 $ from the numerator and denominator:
$$ \frac{1}{-1} $$

3. Simplify to get the final expression:
$$ -1 $$

The excluded value in this case is $ m = 3 $, as it would make the denominator zero, resulting in division by zero, which is undefined.