Question

f(x) = -2x^2 + 5x -1

Find f(x) - f(a)/x-a

Answer 1

I bet you mean

[ f(x) - f(a) ] / (x-a)

Parentheses are VITAL !
f(a) = -2 a^2 + 5 a - 1

so
[ -2(x^2-a^2) +5(x-a) -1+1 ]/(x-a)

= [-2(x-a)(x+a) + 5(x-a) ]/(x-a)

= -2(x+a)+5

Note for future calculus purposes that the limit of this as a approaches a
this becomes
-4 x + 5