SOLUTION: Find the solution set for the equation 3-x/x^2-9=-3 Link to question copy and paste below please , http://prntscr.com/9im26h

Algebra ->  Expressions-with-variables -> SOLUTION: Find the solution set for the equation 3-x/x^2-9=-3 Link to question copy and paste below please , http://prntscr.com/9im26h      Log On


   

Question 1011553: Find the solution set for the equation 3-x/x^2-9=-3 Link to question copy and paste below please ,
http://prntscr.com/9im26h
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%283-x%29%2F%28x%5E2-9%29=-3+
%283-x%29%2F%28%28x-3%29%28x%2B3%29%29=-3+
cross%28%283-x%29%291%2F%28cross%28%28x-3%29%29%28x%2B3%29%29=-3+
1%2F%28x%2B3%29=-3+
1=-3%28x%2B3%29+
1=-3x%2B9+
3x=-1%2B9+
3x=8+
x=8%2F3+-> answer is C


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Find the solution set for the equation 3-x/x^2-9=-3 Link to question copy and paste below please ,
http://prntscr.com/9im26h
%283+-+x%29%2F%28x%5E2+-+9%29+=+-+3, with x+%3C%3E+%22+%22%2B-+3

-+3%28x%5E2+-+9%29+=+3+-+x -------- Cross-multiplying

-+3x%5E2+%2B+27+=+3+-+x

0+=+3x%5E2+-+x+%2B+3+-+27

0+=+3x%5E2+-+x+-+24

0 = (3x + 8)(x - 3)

3x + 8 = 0        OR          x - 3 = 0

3x = - 8          OR          x = 0 + 3

highlight_green%28x+=+-+8%2F3%29          OR          x = 3 (ignore as this is an EXTRANEOUS solution)

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
%283-x%29%2F%28x%5E2-9%29=-3+

The domain of the left side function is all number line except x = +/- 3.
So, in all consideration below x =/= +- 3.

Now factor the denominator:

%283-x%29%2F%28%28x-3%29%28x%2B3%29%29=-3+

Since x =/= 3, we can cancel (x-3) in the numerator and the denominator:

cross%28%283-x%29%291%2F%28cross%28%28x-3%29%29%28x%2B3%29%29=-3+

-1%2F%28x%2B3%29 = -3+

1 = 3%28x+%2B+3%29

1 = 3x+%2B+9+

3x = 1+-+9

3x = -8

x = -8%2F3  -----> answer is B