Simplify the rational expressions. State any excluded values. Show your work.
8.3x-6/x-2
9.x-2/x^2 +3x-10
please.
You will definitely need brackets to properly show these expressions, I will assume you meant:
(3x-6)/(x-2)
= 3(x-2)/(x-2)
= 3, x ≠ 2
You take over to do (x-2)/(x^2 +3x-10)
hint: become very suspicious that perhaps one of the factors in the bottom might be (x-2)
on my exam it shows like fraction way of it with the "___" line in the middle that's why i put "/" so didn't know how to write it but yes that's what i meant :)
and no the (x-2) is on top and the /(x^2 +3x-10) is on the bottom
But I want you to factor the bottom, and my hint was that one of the factors is (x-2)
so (x^2 + 3x - 10) = (x-2)( ...... )
and the x-2 will cancel
so how do i get the answer?
To simplify the rational expressions, we need to simplify the numerator and denominator separately. Let's work through each expression step-by-step:
1) Simplifying the expression 8.3x - 6 / x - 2:
The numerator cannot be simplified further, so let's focus on simplifying the denominator.
The denominator x - 2 is already in the simplest form. However, we need to determine the excluded value, which is the value of x that would make the denominator equal to zero. In this case, x = 2 would result in division by zero, so x = 2 is the excluded value.
Thus, the simplified form of the expression 8.3x - 6 / x - 2 is (8.3x - 6) / (x - 2), with the excluded value x = 2.
2) Simplifying the expression x - 2 / (x^2 + 3x - 10):
Let's factorize the quadratic expression x^2 + 3x - 10, in order to simplify the expression:
x^2 + 3x - 10 = (x + 5)(x - 2)
Now, the expression x - 2 / (x^2 + 3x - 10) can be written as (x - 2) / ((x + 5)(x - 2)).
Notice that (x - 2) appears in both the numerator and denominator. Therefore, it cancels out, simplifying the expression further:
(x - 2) / ((x + 5)(x - 2)) = 1 / (x + 5)
We are left with the simplified expression 1 / (x + 5), without any excluded values.
So, the simplified forms of the given rational expressions are as follows:
1) (8.3x - 6) / (x - 2), with the excluded value x = 2.
2) 1 / (x + 5), without any excluded values.