(x-3)/(x^2-4x+3)
Hello My name is Megan Watt, and I have no idea how to solve this. I am so lost.
Hi Megan, don't worry! I'm here to help you understand how to simplify the expression (x-3)/(x^2-4x+3).
First, let's factorize the denominator (x^2-4x+3). We need to find two numbers that multiply to give 3 and add up to -4.
The factors of 3 are 1 and 3, and the numbers that add up to -4 are -1 and -3. Therefore, the factorization of x^2-4x+3 can be written as (x-1)(x-3).
Now, we can rewrite the expression as (x-3)/[(x-1)(x-3)].
Notice that the numerator (x-3) and the denominator (x-3) have common factors. We can cancel out these common factors. After canceling, we are left with:
1/(x-1)
So, the simplified form of (x-3)/(x^2-4x+3) is 1/(x-1).
I hope this explanation helps! Let me know if you have any further questions.