×-2/×^2+3×-10 i have to write out and find excluded values

Question

I know I got this half right but wanna know how to write or what I'm missing.

Answer 1

×-2/×^2+3×-10 i have to write out and find excluded values

The expression is,

​(x - 2)/(x^2 + 3x - 10)     --   the denominator factorises to give,

(x - 2) / {(x - 2)(x + 5)}    --   cancel out common factors, to give

1 / (x + 5)

For this final expression, x can take any value except x  = -5

For the original expression, (x - 2) / {(x - 2)(x + 5)}, at x = 2, we end up with 0/0 (zero divided by zero), which is not allowed.

So, although we can't give the original expresion a value at x = 2, which makes x = 2 an excluded value, we can give it a limit at x = 2.

Limit [x -> w] (x - 2) / {(x - 2)(x + 5)} = 1/7

Excluded values are: x = 2, x = -5