Another Calculus problem I desperately need help with?

Question

the question is:

Show that f(x) - f(a)/x - a = 3(x + a) where f(x) = 3x^2 - 7.

It says as a hint to combine like terms and factor as much as possible in order to simplify.

I tried it but it's still so confusing..

pleeeeaseee helpp, I'll be so thankful!!!!!!!!!

Answer 1

Do you mean:

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

f(x) = 3x^2 - 7

f(a) = 3a^2 - 7

[3x^2 - 7 - (3a^2 - 7)]/(x - a)

[3x^2 - 7 - 3a^2 + 7]/(x - a)

[3x^2 - 3a^2]/(x - a)

3(x^2 - a^2)/(x - a)

3(x + a)(x - a)/(x - a)

3(x + a)

Next time, make sure you are very clear on the initial equation. It's hard to interpret what you mean without parenthesis in the right places. You're better off using too many parenthesis, rather than too few.

Answer 2

f(x) = 3x² - 7

f(a) = 3a² - 7

subtracting

f(x) - f(a) = 3x²  - 3a²  = 3(x²  - a²) = 3(x-a)(x+a)

divide by (x-a)

{ f(x) - f(a) } / (x-a)  = 3(x+a)

Answer 3

f(x) - f(a)/x - a = 3(x + a) where f(x) = 3x^2 - 7

f(a) = 3a^2 - 7

3x^2 - 7 - (3a^2 - 7)] / (x- a) = 3(x+a)

(3x^2 - 7 - 3a^2 + 7) / (x- a) = 3(x+a)

(3x^2 - 3a^2) / (x- a) = 3(x+a)

3(x^2 - a^2) / (x- a) = 3(x+a)

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

3(x+a) = 3(x+a)