Compute the difference quotient: [(f(x)- f(a))/(x-a)]..

for f(x)= (-1/x^2)

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im sorry, i wrote the question wrong, its supposed to be: f(x)=(-3/x^2), but i think i can follow this same format to solve this one too right?

To compute the difference quotient for the function f(x) = -1/x^2, we can use the definition of the difference quotient and follow these steps:

Step 1: Start with the given function f(x) = -1/x^2.

Step 2: We need to find the value of f(x) and f(a) to substitute them into the difference quotient formula. For this, plug in the values of x and a into the function f(x):

f(x) = -1/x^2
f(a) = -1/a^2

Step 3: Substitute the values of f(x) and f(a) into the difference quotient formula:

[(f(x) - f(a))/(x - a)] = [(-1/x^2) - (-1/a^2)] / (x - a)

Step 4: Simplify the numerator:

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

Step 5: Find a common denominator for the numerator:

[(-a^2 + x^2)/(x^2 * a^2)] / (x - a)

Step 6: Invert the fraction in the denominator and multiply:

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

Step 7: Simplify the numerator:

[-(a^2 - x^2)/(x^2 * a^2)] * (1/(x - a))

Step 8: Factor the numerator:

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

Step 9: Cancel out the common factor of (x - a):

(x + a)/(x^2 * a^2)

So, the difference quotient for the given function f(x) = -1/x^2 is (x + a)/(x^2 * a^2).