HELP!

[debbiewanke]

I need to hand in a take-home test in the morning. There are 10 problems. The last thing that I am doing is trying to get someone else to do my work. I have completed these problems to the best of my ability, but I do not feel that my best is good enough (in math - EVER!!). Please help. I am going to be a nurse and proportions are usually easy for me, so I don't think I'll ever overdose anyone. I just need to get through this course!!! Are these right? HELP!!!!!!!!

#1

X²+X-6/X³ - 27 DIVIDED BY X²-9X+14/X²-8X+15

I got (x+3) (x-5)
(x²+3x+9)(x-7)

#2

(4x-9)/x² - x-12 MINUS (2x-1)/ x² - x – 12

I got 2
X+3

#3

6 / (5x-10) + 3/ (2x² - 8)

I got 6x-27
5(x-2)(x+2)

#4

x³ +5x² - 9x – 45
x³ + 125

I got (x²+5x-9)(x-45)
(x+5)(x²-5x+25)

#5

(x-1)/ (x² +x-6) pLUS (x-2) / (x² + 4x +3)

I got
2x² - 4x + 3
(x+3)(x-2)(x+1)

“solve the next 3”
#6
(3x-4)/6 + 1 / 2 = x/4 + 7 / 12
I got x = 3

#7
(3x+1) / (x-4) = (6x+5) /(2x-7)

I can’t get this one!!!! I got x = -13???

#8

x / 2 - 12/ X = 1


I got x = plus or minus 5

#9

5/3x – 2/x + 3/2
I got 9x-2
6x

#10

5 /3x - 7 / x = 3 / 2

I got x = - 3 5/9

Thank you in advance for your help!
Debbie

 

[Mrspi]

I need to hand in a take-home test in the morning. There are 10 problems. The last thing that I am doing is trying to get someone else to do my work. I have completed these problems to the best of my ability, but I do not feel that my best is good enough (in math - EVER!!). Please help. I am going to be a nurse and proportions are usually easy for me, so I don't think I'll ever overdose anyone. I just need to get through this course!!! Are these right? HELP!!!!!!!!

#1

X²+X-6/X³ - 27 DIVIDED BY X²-9X+14/X²-8X+15

I got (x+3) (x-5)
(x²+3x+9)(x-7)

#2

(4x-9)/x² - x-12 MINUS (2x-1)/ x² - x – 12

I got 2
X+3

#3

6 / (5x-10) + 3/ (2x² - 8)

I got 6x-27
5(x-2)(x+2)

#4

x³ +5x² - 9x – 45
x³ + 125

I got (x²+5x-9)(x-45)
(x+5)(x²-5x+25)

#5

(x-1)/ (x² +x-6) pLUS (x-2) / (x² + 4x +3)

I got
2x² - 4x + 3
(x+3)(x-2)(x+1)

“solve the next 3”
#6
(3x-4)/6 + 1 / 2 = x/4 + 7 / 12
I got x = 3

#7
(3x+1) / (x-4) = (6x+5) /(2x-7)

I can’t get this one!!!! I got x = -13???

#8

x / 2 - 12/ X = 1


I got x = plus or minus 5

#9

5/3x – 2/x + 3/2
I got 9x-2
6x

#10

5 /3x - 7 / x = 3 / 2

I got x = - 3 5/9

Thank you in advance for your help!
Debbie

I'll try to help with a couple of these.

#2

(4x-9)/x² - x-12 MINUS (2x-1)/ x² - x – 12

The denominators are the same...so subtract the numerators and put the result over the common denominator. Simplify if possible.

[(4x - 9) - (2x - 1)] / (x^2 - x - 12)

[4x - 9 - 2x + 1] / (x^2 - x - 12)

The ball is in your court now...combine like terms in the numerator. Factor the denominator. See if there are some common factors that can be divided out.

#4

x³ +5x² - 9x – 45
x³ + 125

I got (x²+5x-9)(x-45)
(x+5)(x²-5)

You can factor the numerator by "grouping." x[sup:1lmogomy]3[/sup:1lmogomy] + 5x[sup:1lmogomy]2[/sup:1lmogomy] - 9x - 45 can be factored by grouping the first two terms together, and the last two terms together. The first two terms have a common factor of x[sup:1lmogomy]2[/sup:1lmogomy]. The last two terms have a common factor of -9. If you remove the greatest common factor from each pair of terms, you'll have

x[sup:1lmogomy]2[/sup:1lmogomy](x + 5) - 9(x + 5)

Do you see that you now have a common factor of (x + 5) in both terms? Remove that common factor, and you'll have

(x + 5)(x[sup:1lmogomy]2[/sup:1lmogomy] - 9]

And x[sup:1lmogomy]2[/sup:1lmogomy] -9 is a difference of two squares, which you can factor as (x + 3)(x - 3)

So....the numerator factors as (x + 5)(x + 3)(x - 3)

The denominator is x[sup:1lmogomy]3[/sup:1lmogomy] + 125

This is a sum of two cubes, because 125 is 5[sup:1lmogomy]3[/sup:1lmogomy]...you should have learned the pattern for factoring this type of expression: a[sup:1lmogomy]3[/sup:1lmogomy] + b[sup:1lmogomy]3[/sup:1lmogomy] = (a + b)(a[sup:1lmogomy]2[/sup:1lmogomy] - ab + b[sup:1lmogomy]2[/sup:1lmogomy])

Factor the denominator, using the pattern for the sum of two cubes. Once the numerator and denominator have been factored, you can reduce by dividing out common factors.

 

[debbiewanke]

Thank you for your help. I believe that I did get the first one right. (2/(x+3)). The second one I got (x+3)(x-3)/x^2 - 5x+25. Just a little direction in the beginning and I usually can get it. The trick is knowing what to do when you see a problem! I am going to a tutor first thing this morning to see if I can get direction with the rest of these. Thank you for your help.