Hi everyone!
I’ve a silly doubt.
Why option E is a polynomial? Yes, it’s polynomial.
If we try to simplify the equation by cross multiplying, we get final expression as 4x^3 – 2x^2 – x = 0 which is a cubic.
I think we can say option E has negative powers only when we simplify it using exponents rule.
What do you think?
That’s not what you get after simplifying E
\frac{1}{x^2} + \frac 2x + 1 = 5 and 4x^2 -2x - 1= 0 indeed share the same solutions, but do their underlying expressions represent the same function?
Namely, are f(x)= \frac{1}{x^2} + \frac 2x - 4 and g(x) = 4x^2 - 2x - 1 equivalent for all values of x in the domain of f?
It might be helpful to just look at the graph of these two functions.
So basically, notice the condition when x=0.
Doesn’t work for option E but works after you have simplified the equation (indicating that the simplified quadratic which you’ve gotten is not the same as option E).
