Simplify the rational expressions. State any excluded values. Show your work.
8.3x-6/x-2
9.x-2/x^2 +3x-10
pleaasee.
Just did this for you in your earlier post
oh i'm sorry i did not see, sorry i'm tired lol
To simplify rational expressions, we need to simplify both the numerator and the denominator separately. Additionally, we need to find any excluded values, which are the values that make the denominator equal to zero, since division by zero is undefined. Let's work through each expression step by step:
Expression 1: (8.3x - 6) / (x - 2)
To simplify the numerator, we can distribute the 8.3 to both terms:
Numerator = 8.3x - 6
The denominator is already in its simplified form: (x - 2)
Now, we need to find the excluded values by setting the denominator equal to zero and solving for x:
x - 2 = 0
x = 2
So, the excluded value for this expression is x = 2.
Therefore, the simplified rational expression is (8.3x - 6) / (x - 2), with the excluded value x = 2.
Expression 2: (x - 2) / (x^2 + 3x - 10)
To factor the denominator, we need to find two numbers that multiply to -10 and add up to +3. The numbers are +5 and -2.
(x^2 + 3x - 10) = (x + 5)(x - 2)
So, the simplified expression becomes (x - 2) / [(x + 5)(x - 2)]
Now, notice that the (x - 2) terms in the numerator and denominator cancel each other out, leaving us with:
1 / (x + 5)
There are no excluded values in this expression since the denominator can never be equal to zero.
Therefore, the simplified rational expression is 1 / (x + 5) for the second expression, with no excluded values.