HELP !!!!
Given the function g(x)=x^2+2x, evaluate (g(x)−g(a))/(x−a), x≠a.
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((x^2+2x) - (a^2+2a))/(x-a)
To evaluate the expression (g(x) - g(a))/(x - a), where g(x) = x^2 + 2x, and x ≠ a, you need to substitute the given expressions into the formula and simplify.
Step 1: Replace g(x) with its expression x^2 + 2x
(g(x) - g(a))/(x - a) = ((x^2 + 2x) - g(a))/(x - a)
Step 2: Simplify g(a) by substituting a into the expression for g(x)
g(a) = a^2 + 2a
Step 3: Substitute the simplified expressions back into the initial formula
((x^2 + 2x) - (a^2 + 2a))/(x - a)
Step 4: Simplify the numerator
(x^2 + 2x - a^2 - 2a)/(x - a)
Step 5: Factorize the numerator if possible
[(x - a)(x + a) - 2(a + 1)] / (x - a)
Step 6: Cancel out the common factor (x - a) from both the numerator and denominator.
(x + a - 2(a + 1))
Step 7: Simplify the numerator
x + a - 2a - 2
Step 8: Combine like terms
x - a - 2
Therefore, the simplified expression is x - a - 2.