Posted by GGIFT on .
When solving a rational equation, why is it necessary to perform a check?

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

ALGEBRA 
Reiny,
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)(x2) = 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 
ALGEBRA 
GGIFT,
I still do not understand it.