SOLUTION: Hi algebra.com! My math teacher totally does not know how to explain math problems. My class has been doing bad on his tests, so my teacher gave us 16 examples of questions that ar

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Hi algebra.com! My math teacher totally does not know how to explain math problems. My class has been doing bad on his tests, so my teacher gave us 16 examples of questions that ar      Log On


   

Question 178319: Hi algebra.com! My math teacher totally does not know how to explain math problems. My class has been doing bad on his tests, so my teacher gave us 16 examples of questions that are going to be on the test. Please solve these problems and show me how to do them. It will be greatly appreciated.The problems
re the following:
1.What is the product of 4x over x-1 and x square - 1 over 3x+3 in simplest form?
2.Simplify and perform the operation: x-3 over x+3 divided by 3x over x square-9?
3.If the length of a rectangular garden is represented by x square +2x over x square + 2x -15 and its width is represented by 2x-6 over x+4, which expression represents the area?
Okay i am going to use / for meaning over or divided by
4.What is the lcd of 1/2, 2/7x, and 5/x?
5.What is the sum of 2/x and x/2?
6.What is the expression y/x - 1/2 equivalent to?
7.What is the value of x in the equation x/2x+1 = 4/3?
8.If 5/n - 1/2 = 3/6n, what is the value of n?
9.Which value of x is a solution of 5/x = x+13/6?
10.Find the lcd of 5/7xcubed times y to the 7th power and 1/4x to the 4th times y to the the 5th.
11.Find the product of x square times 4/7x times and 8x/x+2.
12.Simplify radical 54 + radical 24.
13.Solve radical 4a-3 = radical 3a+1, check your solution.
14.Solve x square + 4x - 60=0 by factoring.
15.Solve by factoring x square - 4x =5.
16.Factor 3x square + 7x - 6.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I think it would be better if you would
work each of these problems. Do a thorough job and someone
may review your work for you and provide feedback.
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Yikes, there are a lot of problems! I'm going to do the first three to get you started. If you're still stuck, then post again or email me.


# 1

%28%284x%29%2F%28x-1%29%29%28%28x%5E2-1%29%2F%283x%2B3%29%29 Start with the given expression.


%28%284x%29%2F%28x-1%29%29%28%28%28x-1%29%28x%2B1%29%29%2F%283x%2B3%29%29 Factor the second numerator


%28%284x%29%2F%28x-1%29%29%28%28%28x-1%29%28x%2B1%29%29%2F%283%28x%2B1%29%29%29 Factor the second denominator


%284x%28x-1%29%28x%2B1%29%29%2F%283%28x-1%29%28x%2B1%29%29 Combine the fractions.


Highlight the common terms.


%284x%2Across%28%28x-1%29%28x%2B1%29%29%29%2F%283%2Across%28%28x-1%29%28x%2B1%29%29%29 Cancel out the common terms.


%284x%29%2F3 simplify



So %28%284x%29%2F%28x-1%29%29%28%28x%5E2-1%29%2F%283x%2B3%29%29=%284x%29%2F3 where x%3C%3E-1 or x%3C%3E1





# 2

%28%28x-3%29%2F%28x%2B3%29%29%2F%28%283x%29%2F%28x%5E2-9%29%29 Start with the given expression.


%28%28x-3%29%2F%28x%2B3%29%29%2A%28%28x%5E2-9%29%2F%283x%29%29 Multiply the first fraction by the reciprocal of the second fraction.


%28%28x-3%29%2F%28x%2B3%29%29%2A%28%28%28x%2B3%29%28x-3%29%29%2F%283x%29%29 Factor the second numerator


%28%28x-3%29%28x%2B3%29%28x-3%29%29%2F%283x%28x%2B3%29%29 Combine the fractions.


%28%28x-3%29highlight%28%28x%2B3%29%29%28x-3%29%29%2F%283x%2Ahighlight%28%28x%2B3%29%29%29 Highlight the common terms


%28%28x-3%29cross%28%28x%2B3%29%29%28x-3%29%29%2F%283x%2Across%28%28x%2B3%29%29%29 Cancel out the common terms


%28%28x-3%29%28x-3%29%29%2F%283x%29 Simplify


%28%28x-3%29%5E2%29%2F%283x%29 Condense the terms.



So where x%3C%3E0, x%3C%3E-3, or x%3C%3E3




# 3

Since "the length of a rectangular garden is represented by x square +2x over x square + 2x -15 and its width is represented by 2x-6 over x+4", this means that L=%28x%5E2%2B2x%29%2F%28x%5E2%2B2x-15%29%29 and W=%282x-6%29%2F%28x%2B4%29


A=LW Start with the area of a rectangle formula


A=%28%28x%5E2%2B2x%29%2F%28x%5E2%2B2x-15%29%29%28%282x-6%29%2F%28x%2B4%29%29 Plug in L=%28x%5E2%2B2x%29%2F%28x%29 and W=%282x-6%29%2F%28x%2B4%29


A=%28%28x%28x%2B2%29%29%2F%28x%5E2%2B2x-15%29%29%28%282x-6%29%2F%28x%2B4%29%29 Factor the first numerator.


A=%28%28x%28x%2B2%29%29%2F%28%28x%2B5%29%28x-3%29%29%29%28%282x-6%29%2F%28x%2B4%29%29 Factor the first denominator.


A=%28%28x%28x%2B2%29%29%2F%28%28x%2B5%29%28x-3%29%29%29%28%282%28x-3%29%29%2F%28x%2B4%29%29 Factor the second numerator.


A=%282x%28x%2B2%29%28x-3%29%29%2F%28%28x%2B5%29%28x-3%29%28x%2B4%29%29 Combine the fractions.


Highlight the common terms


A=%282x%28x%2B2%29cross%28%28x-3%29%29%29%2F%28%28x%2B5%29cross%28%28x-3%29%29%28x%2B4%29%29 Cancel out the common terms


A=%282x%28x%2B2%29%29%2F%28%28x%2B5%29%28x%2B4%29%29 Simplify


A=%282x%5E2%2B4x%29%2F%28%28x%2B5%29%28x%2B4%29%29 Distribute


A=%282x%5E2%2B4x%29%2F%28x%5E2%2B9x%2B20%29 FOIL



So


This means that the area is A=%282x%5E2%2B4x%29%2F%28x%5E2%2B9x%2B20%29