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

Answer 1

When performing operations, like "squaring both sides", sometimes roots are introduced that were not part of the original relation.

e.g.

let x = 4, and only 4
square both sides
x^2 = 16
now take √
√(x^2) = √16
± x = 4
x = ±4 , we now a "new" root

Answer 2

So inother words, we need to make that solutions are not those of original equations??

Answer 3

I will give you another example

solve √(3x+10) = x+2
square both sides
3x+10 = x^2 + 4x + 4
x^2 + x - 6 = 0
(x+3)(x-2) = 0
x = -3 or x = 2

check: (in original)
if x=2
LS = √(6+10) = √16 = 4
RS = 2+2 = 4 , checks

if x = -3
LS = √(-9+1) = 1
RS = -3+2 = -1 , does not work

so x = 2

Answer 4

I still do not understand it.