Given equation,which value must you assign to a so that f(x) is continuous at x=1?

I think that you probably intended the denominator to be the quantity " x - 1 ". If so, you need to remember to put it in parentheses.

Proceeding from there, the reason that f(1) has to be defined is because the expression (x^2 + x - 2) / (x - 1) has a zero denominator when x = 1.

Noting that x^2 + x - 1 is factorable as (x + 2)(x - 1), the fraction reduces to f(x) = x + 2 when x is not equal to 1.

Linear functions are continuous on their domains so f(x) will be continuous at x = 1 if we define f(1) = 1 + 2 = 3.

Therefore, a = 3

y = (x^2+x-2) / (x-1) will simplify algebraically to y = x + 2
so add
f(1) = 3 to the function definition

in other words,
3 if x = 1

f(x) = x+2 if x not equal to 1
--->a = 1+2=3