Tutor: Hi! I am now working on your question and you will soon see me writing on your drawing board.
Tutor: Did I write the equation correctly?
Student: Yes, thanks
Tutor: We'll simplify the equation first
Tutor: We'll do that by dividing numerator and denominator by 2
Tutor: What is the value when you simplify 2x/2?
Student: X?
Tutor: That's perfect!
Tutor: What is the value when you simplify 6/2?
Student: 3?
Tutor: Great
Tutor: Now... We will find values of x that make the function f(x) be undefined
Tutor: This function will become undefined when the numerator becomes 0, since we can't divide by 0.
Tutor: What is the value that makes the denominator 0?
Tutor: I mean, what is the value of x that makes the denominator equal to 0?
Student: 3?
Tutor: That's correct!
Tutor: That means the domain will be all values of x except 3.
Tutor: That's the answer.
Tutor: Are there any more questions that I can help you with?
Student: Wow-that wasn't so bad with you walking me through it -
Student: Can we do one more?
Tutor: Yes, of course.
--- Page 2 ---
Tutor: I'm ready to continue when you are.
Student: 2/x+4/3=1
Tutor: We'll start by moving 4/3 to the right side of the equation.
Tutor: For that, we'll subtract 4/3 on both sides.
Tutor: Then we simplify...
Tutor: What is the value we get on the left side of the equation?
Student: 2/x?
Tutor: That's correct!
Tutor: What is the value we get on the right side of the equation?
Student: -1/3
Tutor: Great!
Tutor: Now, we'll move the x to the numerator.
Tutor: To do so we have to multiply by x
Tutor: What is the value we get after simplifying the left side of the equation?
Student: 2
Tutor: That's correct!
Tutor: Now we have the x on the right side. But we have a minus and a three on the same side.
Tutor: We need to have the x alone so we get the answer.
Tutor: What is the value have to multiply to remove the 3 from the denominator?
Student: Time by negative 3 to move to the right side
Tutor: Perfect!
Tutor: The small x is actually a product
Tutor: What is the value we get when we simplify on the left side?
Student: -6
Student: = x
Tutor: Perfect!
Tutor: And that's the answer
Tutor: Are there any more questions that I can help you with?
Student: One more please
--- Page 3 ---
Tutor: Of course, please type the question here.
Student: Can we find zero of 2x^3 + 3x^2 +x
Tutor: Yes, of course.
Student: Thanks
Tutor: One thing we can do is factoring out terms from the expression.
Tutor: A common first step to factoring is taking a common factor out.
Tutor: What is the value of the common factor between the terms 2x^3, 3x^2 and x?
Student: X?
Tutor: Perfect!
Tutor: Now we have to write each term with the x taken out.
Tutor: To do so we divide each term by the common factor (x)
Tutor: What is the value of dividing 2x^3 over x?
Student: 2x^2?
Tutor: That's perfect!
Tutor: What is the value when we divide 3x^2 over x?
Student: 3x
Tutor: That's correct!
Tutor: What is the value when we divide x over x?
Student: 1
Tutor: Correct!
Tutor: Now... we can find the first 0 of the expression.
Tutor: Notice that there is a product here
Tutor: Those are two factors multiplied
Tutor: If any of those factors become 0, the whole product will become 0
Tutor: What is the value that makes the first factor 0?
Student: Don't get it-sorry
Tutor: Ok
Tutor: We have a product of two factors. Is that correct?
Student: Ok
Tutor: We have X times (2x^2+3x+1)
Student: Got it
Tutor: If any of those factors becomes 0, the product will be 0, because 0 times anything is 0
Tutor: Then, what is the value of X that will make the first factor 0?
Student: X=0
Tutor: Perfect!
Tutor: That's the first zero of the expression
Tutor: I wrote it down, it is part of the final answer.
Tutor: But we still may be able to find more.
Student: Ok
Tutor: Let's see what makes the second 0
Tutor: Do you know any method to find zeros of a quadratic?
Student: Wouldn't we just move the 1 to the right - I don't remember what that function is called
Tutor: Ok...
Tutor: There are several methods.
Student: Ok
Tutor: Let me know if any rings a bell. The names are:
Tutor: Quadratic formula
Tutor: AC method
Tutor: Completing squares
Tutor: Do you remember hearing about any of those names?
Student: Yea the quadratic formula is x= -b squar root of b - 4(a)(c) /2(a) right
Tutor: Yes! That's correct!
Tutor: What is the value of a in our formula?
Student: 2
Tutor: Perfect!
Tutor: What is the value of b?
Student: 3
Tutor: What is the value of c?
Student: 1
Tutor: Perfect!
Tutor: Let's simplify now...
Tutor: What is the value of 3 squared minus 4 times 2 times 1?
Student: 1
Tutor: And what is the value of 2 times 2?
Tutor: :)
Student: 4
Tutor: Great!
Tutor: What is the value of square root of 1?
Student: 1
Tutor: Great
Tutor: Now let's find both values of x
Tutor: What is the value of -3 + 1 over 4?
Student: -2/4
Tutor: Great
Student: Or -1/2
Tutor: :)
Tutor: Exactly
Tutor: What is the value of -3-1 over 4?
Student: -1
Tutor: Perfect!
Tutor: That gives us our solution
Tutor: X=0, x=-1/2 and x=-1
Tutor: Do you want us to check the solutions?
Student: Thanks alot-its much clearer now - am good; can plug in to check on my own - needed your help to get here!
Tutor: :) Great
Tutor: Are there any more questions that I can help you with?
Student: Thanks so much for your time - you're an excellent instructor!
Tutor: Thank you :)
Tutor: Good bye. Thank you for using Instant Math Help.
Student: Student has ended this session. This question is automatically marked as done.
