(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! I'm here to help you solve the expression (x-3)/(x^2-4x+3).
To simplify this expression, we need to factorize the denominator, x^2-4x+3, and then cancel out any common factors between the numerator and denominator.
First, let's factorize the denominator by breaking down the quadratic equation x^2-4x+3 into two binomials. We are looking for two numbers that add up to -4 (the coefficient of x) and multiply to give 3 (the constant term). The numbers are -1 and -3, so we can rewrite the equation as:
x^2 - 4x + 3 = (x - 3)(x - 1)
Now, let's substitute the factored form of the denominator back into the original expression:
(x - 3)/(x^2 - 4x + 3) = (x - 3)/((x - 3)(x - 1))
Now, we can see that we have (x - 3) in both the numerator and denominator. These can be canceled out, leaving us with:
(x - 3)/(x^2 - 4x + 3) = 1/(x - 1)
Therefore, the simplified form of the expression (x-3)/(x^2-4x+3) is 1/(x - 1).
I hope this explanation helps! Let me know if you have any more questions.