SOLUTION: For what value of x is the rational expression below equal to zero? x-1/(x-3)(x+1)

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Question 1027248: For what value of x is the rational expression below equal to zero?
x-1/(x-3)(x+1)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Expression as given or asked here,
x-1/(x-3)(x+1)

Appears when rendered,
x-1%2F%28x-3%29%28x%2B1%29

Raise to equivalent in higher terms,
x%28%28x-3%29%28x%2B1%29%29%2F%28%28x-3%29%28x%2B1%29%29-1%2F%28x-3%29%28x%2B1%29

%28x%28x%5E2-2x-3%29-1%29%2F%28%28x-3%29%28x%2B1%29%29

%28x%5E3-2x%5E2-3x-1%29%2F%28%28x-3%29%28x%2B1%29%29=0
Your interest is now to find the REAL roots of the NUMERATOR. Start with synthetic division to check on the roots, -1, and 1, probably the only possible real roots but there MIGHT be irrational roots, also real. 


-1      |     1    -2    -3    -1
        |          -1    3     0
        |________________________________
             1     -3    0     -1          Not a root


1       |     1     -2     -3    -1
        |
        |            1     -1    -4
        |________________________________
             1      -1     -4     -5       Not a root

Use any other methods you know. You could try a graphing tool.

graph%28400%2C400%2C-5%2C5%2C-10%2C10%2Cx%5E3-2x%5E2-3x-1%29
This appears to show two real roots but they are irrational. This seems strange.

Try a closer look:
graph%28400%2C400%2C-2%2C4%2C-3%2C3%2Cx%5E3-2x%5E2-3x-1%29
Only ONE Real, irrational root, and it is slightly greater than 3.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

For what value of x is the rational expression below equal to zero?
x-1/(x-3)(x+1)