Simplifing rational expressions
Simplify the expression & state any excluded values:
(2s^2 - 5s - 12) / (2s^2 - 9s + 4)
2s^2-9s+4 = (2s-1)(s-4)
so the denominator is zero when x = 1/2 or 4
2s^2-5s-12 = (2s+3)(s-4)
so, I guess it's clear now what the simplified quotient is, eh?
I should know, eh? Thanks, Steve
To simplify the rational expression, we can factor both the numerator and the denominator of the fraction.
Let's start by factoring the numerator:
(2s^2 - 5s - 12)
We need to find two numbers that multiply to give -12 and add up to -5. The numbers -8 and 3 satisfy these conditions:
(2s^2 - 8s + 3s - 12)
Now, we group the terms:
[(2s^2 - 8s) + (3s - 12)]
Next, we factor out the greatest common factor from each group:
[2s(s - 4) + 3(s - 4)]
Now, we have a common binomial factor of (s - 4):
(2s + 3)(s - 4)
Moving on to the denominator:
(2s^2 - 9s + 4)
This can be factored as:
(2s - 1)(s - 4)
Therefore, the expression simplifies to:
(2s + 3) / (2s - 1)(s - 4)
Now, let's determine the excluded values, if any.
To identify the excluded values, we need to look for values of "s" that would make the denominator equal to zero. In this case, the factors (2s - 1) and (s - 4) should not be equal to zero.
Setting each factor to zero and solving for "s," we find:
2s - 1 = 0 => 2s = 1 => s = 1/2
s - 4 = 0 => s = 4
Therefore, the excluded values for "s" are 1/2 and 4, as they would make the denominator equal to zero.