Question

When solving a rational equation, why is it necessary to perform a check?

Answer 1

because if you get multiple answers you can find out if one doesn't work

Answer 2

Because the function "x squared" isn't injective. Look at it this way: the equation\[\sqrt{2-x} = x\]and the equation\[-\sqrt{2-x}=x\]both become\[2-x=x^2\]when squared. The solutions of this quadratic equation are\[x = -2, x = 1\]but the original equations are clearly different, so they must have different solutions. Each of these solutions solves only one of the equations. When you square an equation you "lose" information about the original equation (by knowing that the squared equation is\[2-x=x^2\]you cannot know which is the original equation), therefore you must perform a check.

Answer 3

so you can make sure you dont have the wrong answerr :P