Why is 1/x^2 + 2/x +1 = 5 not a quadratic equation?
Can I not take the LCM as x^2 thus giving me 1+ 2x + x^2 = 5x^2
And simplify it to 4x^2 - 2x - 1 = 0?
According to the PrepSwift quiz on quadratic solutions, this is the explanation: Option E is not even a polynomial due to the presence of negative powers. This is also not a quadratic.
Consider the original equation. Is that a quadratic?
The original is not a quadratic equation but it can be simplified to make it a quadratic equation without negative powers. This is tricky and confusing, do we consider the original equation or after doing some operations on it?
For those equations were we have negative powers and cannot be simplified further, are not quadratic equations. But what about such cases?
You must consider the original equation. Otherwise you could convert for example the linear equation x = 1 into the quadratic x^2 = x by multiplying x on both sides.