SOLUTION: FUNMATH- please help!! 35. 4/x+3 + 7/x^2 - 3x + 9 = 108/x^3 + 27 39. x-1/3 + 6x+1/15 + 2(x-2)/13-7x = 2(x+2)/5 41. f(x) = 2x - 6/x; f(x) = 1 45. f(x) = 6/x - 6/2x: f(x) = 5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: FUNMATH- please help!! 35. 4/x+3 + 7/x^2 - 3x + 9 = 108/x^3 + 27 39. x-1/3 + 6x+1/15 + 2(x-2)/13-7x = 2(x+2)/5 41. f(x) = 2x - 6/x; f(x) = 1 45. f(x) = 6/x - 6/2x: f(x) = 5      Log On


   



Question 60826This question is from textbook Intermediate Algebra 9th
: FUNMATH- please help!!
35. 4/x+3 + 7/x^2 - 3x + 9 = 108/x^3 + 27
39. x-1/3 + 6x+1/15 + 2(x-2)/13-7x = 2(x+2)/5
41. f(x) = 2x - 6/x; f(x) = 1
45. f(x) = 6/x - 6/2x: f(x) = 5
This question is from textbook Intermediate Algebra 9th

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
4/(x + 3) + 7/(x^2 - 3x + 9) = 108/(x^3 + 27)
4/(x + 3) + 7/(x^2 - 3x + 9) = 108/((x + 3)(x^2 - 3x + 9))
4((x + 3)(x^2 - 3x + 9))/(x + 3) + 7((x + 3)(x^2 - 3x + 9))/(x^2 - 3x + 9) = 108((x + 3)(x^2 - 3x + 9))/((x + 3)(x^2 - 3x + 9))
4(x^2 - 3x + 9) + 7(x + 3) = 108
4x^2 - 12x + 36 + 7x + 21 = 108
4x^2 - 6x - 51 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-6x%2B-51+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A4%2A-51=852.

Discriminant d=852 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+852+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+852+%29%29%2F2%5C4+=+4.39862987983161
x%5B2%5D+=+%28-%28-6%29-sqrt%28+852+%29%29%2F2%5C4+=+-2.89862987983161

Quadratic expression 4x%5E2%2B-6x%2B-51 can be factored:
4x%5E2%2B-6x%2B-51+=+4%28x-4.39862987983161%29%2A%28x--2.89862987983161%29
Again, the answer is: 4.39862987983161, -2.89862987983161. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-6%2Ax%2B-51+%29


They are relatively the same.