You're right, but that doesn't give the working...
These might help you get your head round it, though they don't show the exact same problem:
here and
here.
Disclaimer - I haven't done any algebra since about 1980, and never had to do anything with absolute values, even in my university course in engineering science.What I would do is remove the absolute value bars from the equation. This can be done without squares and stuff by looking at different ranges of x values. Split the equation into two:
y = |x+1| + |x-1|
y = 2
Then to simplify the first, split into three versions for the possible signs of the expressions inside the absolute bars:
for x<-1, (x+1) and (x-1) are both negative, so you have: y = -(x+1) + -(x-1) giving y = -2x
for x>=1, (x+1) and (x-1) are both positive, so you have: y = (x+1) + (x-1) giving y = 2x
for -1<=x<1, (x+1) is positive and (x-1) is negative, so you have: y = (x+1) + -(x-1) giving y = 2
from which you can see that the equation is true for all x in the interval -1 to 1.
How you are actually expected to show it, I have no idea, though! There's probably a more systematic way of expressing it.
(edit) Oh look, this approach is described
here 
√(x+1)² + √(x-1)² = 2
(x² + 2x + 1) + (x² - 2x + 1) = 4
This step is wrong; you have squared each term on the left rather than the whole expression.
