simplify the difference quotient

Question

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

for the given function  f(x)=4-3x-x^2

Answer 1

f(x) = 4 - 3x - x²

 

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

 

= [(4 - 3x - x²) - (4 - 3a - a²)] / (x - a)

 

= (-3x - x² + 3a + a²) / (x - a)

 

= [-3(x - a) - (x + a)(x - a)] / (x - a)

 

= -3 - x - a