SOLUTION: Solve the equation algebraically. (7/(x-7))+(3/(x+2)=(9x)/(x^2-5x-14)

Algebra ->  Rational-functions -> SOLUTION: Solve the equation algebraically. (7/(x-7))+(3/(x+2)=(9x)/(x^2-5x-14)      Log On


   

Question 1126015: Solve the equation algebraically.
(7/(x-7))+(3/(x+2)=(9x)/(x^2-5x-14)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


%287%2F%28x-7%29%29%2B%283%2F%28x%2B2%29%29=%289x%29%2F%28x%5E2-5x-14%29

x=7 and x=-2 are excluded from the domain.

Multiply through by the common denominator and solve:

7%28x%2B2%29%2B3%28x-7%29+=+9x
7x%2B14%2B3x-21+=+9x
x+=+7

The algebraic solution to the equation is one of the values that is excluded from the domain, so the equation has no solution.

Here is a graph of the DIFFERENCE between the two expressions in the equation; if there were a solution to the equation, this graph would show 0 at some point.

You can see the vertical asymptote at x = -2. At x=7 there is only a single point "hole" in the graph; this graphing utility does something strange to show it...!