Need help with these 4 College Algebra problems

[sophie19]

\(\displaystyle \displaystyle 3+ \frac{1}{x}/\displaystyle 4+ \frac{1}{x^2}\mbox{simplify the complex fraction}\)

\(\displaystyle \frac{x^2+ 9x+20}{4x^2- 19x+21}/\frac{x^2- 16}{x^2- 6x+9} \mbox{Perform indicated operation and simplify}\)

\(\displaystyle \displaystyle \left(\frac{4}{9}\right)^\frac{3}{2}\mbox{simplify the numerical expression}\)

\(\displaystyle \displaystyle \left (\frac{-36a^{-1}b^{-6}}{4a^{-1}b^4}\right)^{-2}\mbox{simplify the expression}\)

Now before you say why don't I try them myself instead of getting easy help let me just say I had a horrible math teacher (couldn't teach for his life) for this fall semester :x (I'm in college) and tomorrow I have a final that I have been studying for like crazy but these 4 problems are just driving me insane. So please help and just don't give answer but thorough step by step how to do each problem so that I can actually learn how to do these math problems for once

P.S learning this Latex text code system is fun took me 3 hours to finally post my problems but I figured that this way it will be clearer for anybody that wishes to help me

 

[mmm4444bot]

Do you have a textbook?

There should be examples for each type of exercise.

I think your 3-hour time investment on learning LaTex coding is a waste of your time; that's three hours that you could have spent reading your textbook. (Perhaps, the issue is not with your teacher.)

For your first exercise, combine the two terms in the numerator into a single fraction. Do the same thing with the denominator. Use the rule that dividing by a fraction is the same as multiplying by its reciprocal to write the expression as a product. Simplify.

Use the same rule on your second exercise (i.e., rewrite the expression as a product by multiplying by the reciprocal of the ratio on the bottom). Next, factor the polynomials, and simplify.

On the third exercise, raising to the power of 3/2 is the same as taking the square root and then cubing. Apply this exponent to both the numerator and denominator because the entire fraction is the base.

For the fourth exercise, do you know that -36/4 is equal to -9? That's fairly basic. There is also an obvious cancellation with the powers of a. Look up rules and properties for exponents to handle the powers of b and the outer exponent of -2.

If you need more help with any of these, then either show your work or explain why you're stuck.

 

[sophie19]

K well let me just simplify that the current math textbook I have is the worse textbook I have every seen for math if I could get the one I had in high school I would probably understand the problems better. Now the only reason why I spent 3 hours doing something else then math is so that I don't go crazy because I have been studying intensively from Friday (looking up online lots of info and attempting many different problems). Also the way you posted your reply I'm sorry I can't quite understand what you mean , this is also in part to do with the fact that I am a visual learner so I have to see the problem step by step so I can see how you came to that answear.

 

[mmm4444bot]

You wrote: 3 + 1/x

I wrote: combine these two terms into a single fraction

You wrote: I don't understand what you mean

I write: Rewrite 3/1 as an equivalent fraction with a denominator of x. Once you have two fractions with a common denominator, you can add the two fractions by adding the numerators and writing their sum over the common denominator.

Can you add 3 + 1/x now?

 

[Denis]

... this is also in part to do with the fact that I am a visual learner ,,,

Well, if you're "visual", you're asking us to teach without a blackboard...impossible here.

I can show you #3, since reasonable typing (which I hate!) is required:
RULE: (a^b)^c = a^(bc)
So (4/9)^(3/2) = [(4/9)^(1/2)]^3 : 1/2 times 3 = 3/2, right?
(4/9)^(1/2) = 2/3
(2/3)^3 = 8/27 : kapish?

Good luck.