Perform indicated operations and simplify

S

ScienceJen

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Hi everyone - I think this is considered beginning algebra. I'm brushing up on this because I'm taking calculus, and I need help on number 28 - please and thank-you. If you also feel like doing #27, I would appreciate that.

- Jen

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Multiply each term by [imath](c-1)[/imath]
 
For 28 where are you having problems? We can help you better if you tell us where your problem is. For example, do you know how to simplify
[imath]\dfrac{1}{ 1 + \dfrac{1}{1 + x} }[/imath]

-Dan
 
topsquark said:
For 28 where are you having problems? We can help you better if you tell us where your problem is. For example, do you know how to simplify
[imath]\dfrac{1}{ 1 + \dfrac{1}{1 + x} }[/imath]

-Dan
Click to expand...
Hi Dan,

I'm not sure where to begin. The fraction in the denominator is throwing me off. Do I multiply the reciprocal? I think what I did was multiply the denominator by the denominator and the numerator - same as if I were trying to rationalize the denominator, but I forgot to change the + to a - sign.

Thanks again,

Jen
 
Simplify the numerator, then simplify the denominator then and only then simplify the fraction.
 
ScienceJen said:
Hi Dan,

I'm not sure where to begin. The fraction in the denominator is throwing me off. Do I multiply the reciprocal? I think what I did was multiply the denominator by the denominator and the numerator - same as if I were trying to rationalize the denominator, but I forgot to change the + to a - sign.

Thanks again,

Jen
Click to expand...
Big hint: [imath]\dfrac{1}{1 + \dfrac{1}{x + 1} } \cdot \dfrac{x + 1}{x + 1} =[/imath]

-Dan
 
ScienceJen said:
Oh, yes. I get that now, thank you. My "final answer" is -1/2.
Click to expand...
Please share "steps" you took to reach your answer. We would like to guide you to the correct answer - once we know where to "fix" our attention.
 
Steven G said:
Do you really think that no matter what the value of c is, the fraction will always be -1/2? You have to believe that if you think that the answer is -1/2.
Click to expand...
This reminds me of a simple "sanity check": whichever answer you get, pick an arbitrary [imath]c[/imath] and check whether both the original and the simplified expressions get the same value.
 
Steven G said:
Simplify the numerator, then simplify the denominator then and only then simplify the fraction.
Click to expand...
I never thought of multiplying as simplifying, but I guess that's what it is sometimes. Thank you.

lookagain said:
That is not correct. What does the numerator simplify to? What does the denominator simplify to?
Click to expand...
I get c-1+1 for the numerator and c-1-1 for the denominator. Next I got c-1+1 = c for the numerator and c-1-1 = c-2 for the denominator. I thought then that the c in the numerator and the c in the denominator would cancel out, leaving me with -1/2. I'm not sure what I'm doing wrong. Thank you for all of your help! My "tutor" (online instructor for introductory calculus) has informed me that he has 160 students and told me I need to "'dig my heels in more and try to figure it out on my own."' I just need to know the basic concepts and then I'm sure it will "click," as math needs to do.
Thank you so much for your help, everybody!

Subhotosh Khan said:
Please share "steps" you took to reach your answer. We would like to guide you to the correct answer - once we know where to "fix" our attention.
Click to expand...
I get c-1+1 for the numerator and c-1-1 for the denominator. Next I got c-1+1 = c for the numerator and c-1-1 = c-2 for the denominator. I thought then that the c in the numerator and the c in the denominator would cancel out, leaving me with -1/2. I'm not sure what I'm doing wrong. Thank you for all of your help! My "tutor" (online instructor for introductory calculus) has informed me that he has 160 students and told me I need to "'dig my heels in more and try to figure it out on my own."' I just need to know the basic concepts and then I'm sure it will "click," as math needs to do.
Thank you so much for your help, everybody!

Steven G said:
Do you really think that no matter what the value of c is, the fraction will always be -1/2? You have to believe that if you think that the answer is -1/2.
Click to expand...
Hmmm....never thought of that before...well, no. It looks like "should be" -1, but I don't know if that's right or how to get there. I know this is a simple equation and that I'm missing some sort of step or concept.
Thank you.

Wait a seo
ScienceJen said:
Hmmm....never thought of that before...well, no. It looks like "should be" -1, but I don't know if that's right or how to get there. I know this is a simple equation and that I'm missing some sort of step or concept.
Thank you. ....
Click to expand...
Wait a second....if it's c-1+1/c-1-1...then, the c on numerator and c on denominator cancel out and -1s will cancel out...leaving us with -1??? :unsure:

topsquark said:
Big hint: [imath]\dfrac{1}{1 + \dfrac{1}{x + 1} } \cdot \dfrac{x + 1}{x + 1} =[/imath]

-Dan
Click to expand...
Thank you.
 
ScienceJen said:
Oh, yes. I get that now, thank you. My "final answer" is -1/2
Click to expand...

ScienceJen said:
Wait a seo

Wait a second....if it's c-1+1/c-1-1...then, the c on numerator and c on denominator cancel out and -1s will cancel out...leaving us with -1??? :unsure:
Click to expand...
Please use parenthesis. [imath]c - 1 + 1/c - 1 -1 = c - 1 + \dfrac{1}{c} -2[/imath].

[imath]\dfrac{c - 1 + 1}{c - 1 - 1} = \dfrac{c}{c - 2}[/imath]

You can only cancel the c's if both the numerator and denominator have factors of c in them. [imath]\dfrac{c}{c - 2} \neq \dfrac{1}{-2}[/imath]. Try it for a couple of values of c if you don't see this.

-Dan
 
topsquark said:
Please use parenthesis. [imath]c - 1 + 1/c - 1 -1 = c - 1 + \dfrac{1}{c} -2[/imath].

[imath]\dfrac{c - 1 + 1}{c - 1 - 1} = \dfrac{c}{c - 2}[/imath]

You can only cancel the c's if both the numerator and denominator have factors of c in them. [imath]\dfrac{c}{c - 2} \neq \dfrac{1}{-2}[/imath]. Try it for a couple of values of c if you don't see this.

-Dan
Click to expand...
Yeah, I see if I substitute c = 3 into the equation, I can see that it will not equal -1/2. Thank you.
 
ScienceJen said:
So, I guess the answer is (c/c-2) then?
Click to expand...
No!

The correct expression is c/(c-2)

Those parentheses are SUPER IMPORTANT and must be included and must be placed in correct position.

Now tackle #28 in a similar way.
 
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