SOLUTION: Hello there hope you could help me to answer my homework. Please help me to solve this with solution . 1. (x-4)/(x^3-7x^2+2x+40) Thanks, Desiree

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello there hope you could help me to answer my homework. Please help me to solve this with solution . 1. (x-4)/(x^3-7x^2+2x+40) Thanks, Desiree       Log On


   

Question 975014: Hello there hope you could help me to answer my homework.
Please help me to solve this with solution .
1. (x-4)/(x^3-7x^2+2x+40)
Thanks,
Desiree
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-4%29%2F%28x%5E3-7x%5E2%2B2x%2B40%29

Divide numerator and denominator by the numerator x-4

Either long division or by synthetic division:

            x² -  3x - 10
x - 4)x³ - 7x² +  2x + 40
      x³ - 4x²
          -3x² +  2x
          -3x² + 12x
                -10x + 40
                -10x + 40

or  

4 | 1 -7   2  40
  |    4 -12 -40
    1 -3 -10   0

either way the denominator factors as

%28x-4%29%2F%28%28x-4%29%28x%5E2-3x-10%29%29

Then as long as x is not 4, we can cancel (x-4)

cross%28%28x-4%29%29%2F%28cross%28%28x-4%29%29%28x%5E2-3x-10%29%29

1%2F%28x%5E2-3x-10%29

You can leave it like that or factor the denominator:

1%2F%28%28x-5%29%28x%2B2%29%29

Edwin