Expert: Sherman D. - 7/5/2004

Question
1.)  x^2/2 - 7x/6= 1

2.)  Find all values of k so that t^2 + kt-8 can be factored using integers.  

3.) 4n^2/2n+3 - 9/2n+3

3.) 5w^2y^2/8v^4 x n^3/n-4

4.)  9r^5u/m^6 divided by (3r^3m^2  

Answer
If by these you mean

1.)
((x^2)/2) - ((7x)/6) = 1
Multiply everything by 6
3x^2 - 7x = 6
3x^2 - 7x - 6 = 0
Using the quadratic formula
x = (-b ± sqrt(b^2 - 4ac))/2a
x = (-(-7) ± sqrt((-7)^2 - 4(3)(-6)))/2(3)
x = (7 ± sqrt(49 + 72))/6
x = (7 ± sqrt(121))/6
x = (7 ± 11)/6
x = (18/6) or (-4/6)

x = 3 or (-2/3)

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2.)
Find all values of k so that t^2 + kt-8 can be factored using integers.
t^2 + kt - 8
4 and -2
2 and -4
8 and -1
-1 and 8
are possible factors, but to keep "k" positive,
4 and -2
or
8 and -1
would work because 4 is higher than 2, and 8 is higher than 1.
So you get "k" is 2 and 7
so this would give you the problems
t^2 + 7t - 8 or t^2 + 2t - 8
however if the "k" being positive doesn't matter,t hen the other numbers would be "k" is -2 and -7
so this would give you
t^2 - 2t - 8 and t^2 - 7t - 8
so in otherwords, you get

"k" is ±2 or ±7

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3.)
((4n^2)/(2n + 3)) - (9/(2n + 3))
Since both the 4n^2 and 9 have the same denominator, you can say
(4n^2 - 9)/(2n + 3)
factor the numerator
((2n - 3)(2n + 3))/(2n + 3)
since there is a (2n + 3) on top and bottom, the cancel out, so your answer is

2n - 3

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To let you know, in algebra, no one uses "x" to mean multiply, because it could be confused as a variable, so we just use * or • when typing * is used.

4.)
((5w^2y^2)/(8v^4)) * ((n^3)/(n - 4))
Multiply across
(5n^3w^2y^2)/(8v^4n - 32v^4)
or
(5/8)((n^3w^2y^2)/(nv^4 - 4v^4)
however if you meant to say
((5w^2y^2)/(8v^4)) * ((n^3)/(n^-4))
then this becomes
((5w^2y^2)/(8v^4)) * ((n^3)/((1/(n^4)))
becomes
((5w^2y^2)/(8v^4)) * (n^3 * n^4)

(5n^7w^2y^2)/(8v^4)

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5.)
9r^5u/m^6 divided by (3r^3m^2)
((9r^5u)/(m^6)) / (3r^3m^2)
becomes
((9r^5u)/(m^6)) / ((3r^3m^2)/1)
multiply top half by reciprocal of bottom half
((9r^5u)/(m^6)) * (1/(3r^3m^2))
Multiply across
(9r^5u)/(3r^3m^8)
becomes
((9r^5)/(3r^3)) * (u/(m^8))
Simplifies to
(3r^2) * (u/(m^8))
becomes

(3r^2u)/(m^8)

if you have any questions, just let me know.