If x 0 and x - (2- x^2)/x = y/x, then y =

Question

If x ≠ 0 and x - (2- x^2)/x = y/x, then y =

A. − 2 − 3x^2
B. x^2 − 2
C. 2x^2 − 2
D. x − 2 − x^2
E. x − 2 + x^2

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harjas2222 · Answer

I might be wrong

x( x - (2-x^2)/x) = y/x

x^2 - 2 + x^2 = y

2x^2 + 2 = y ?

c? am i wrong? did i fall for a trap here?

Dereno · Answer

x - (2- x^2)/x = y/x

/ x = y/x

x^2 - (2- x^2) = y

x^2 -2 + x^2 = y

2x^2 - 2  = y

Option C

luisdicampo · Answer

Given the equation:
 x - \frac{2 - x^2}{x} = \frac{y}{x}

To isolate  y , we can multiply the entire equation by  x  (since  x 
eq 0 ).

Multiply each term by  x :
 x(x) - x\left(\frac{2 - x^2}{x}ight) = x\left(\frac{y}{x}ight)

Simplify:
 x^2 - (2 - x^2) = y

Now, distribute the negative sign across the parentheses:
 x^2 - 2 + x^2 = y

Combine like terms ( x^2 + x^2 ):
 2x^2 - 2 = y

This matches option (C).

Answer: C

Retakesthegmah · Answer

It unclear is y/x = (x-(2-x^2))/x or x - ((2-x^2)/x) just based on the question

Bunuel · Answer

x - (2- x^2)/x can only mean   x - \frac{2- x^2}{x} . So, all is good there.

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