SOLUTION: Determine whether the given x-value is a solution of the equation. x/2x+1 = 5/4-x^2 , x=-1 True False

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Question 891622: Determine whether the given x-value is a solution of the equation.
x/2x+1 = 5/4-x^2 , x=-1
True
False
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the equation is really
x/(2x+1)= 5/(4-x^2) or x%2F%282x%2B1%29=+5%2F%284-x%5E2%29 .
(If you cannot write the 2x%2B1 and the 4-x%5E2 as denominators,
under long horizontal lines,
the only way to show that those deonminators need to be calculated first is to wrap them in parentheses).
Substituting x=-1 into that equation we get
1%2F%282%2A%28-1%291%2B1%29=+5%2F%284-%28-1%29%5E2%29 , which is
1%2F%28-2%2B1%29=5%2F%284-1%29 ,
1%2F-1=5%2F3 , and
-1=5%2F3 .
That is false.

The equation you wrote is
x/2x+1 = 5/4-x^2 or x%2F2x%2B1+=+5%2F4-x%5E2 ,
which is different, because without the parentheses,
x%2F2x=1%2F2 is calculated first, before adding 1 .
For that equation, substituting x=-1 gives us
%28-1%29%2F2%28-1%29%2B1+=+5%2F4-%28-1%29%5E2 , which is
1%2F2%2B1+=+5%2F4-1 , and
3%2F2+=-1%2F4 .
That is also false.