# If F(x)=x^2+5x how do I find in simplest form F(p)-F(q)/p-q ?

find:

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To find (\frac{F(p) - F(q)}{p - q}), where (F(x) = x^2 + 5x), substitute (p) and (q) into (F(x)) to find (F(p)) and (F(q)). Then simplify the expression by applying the difference quotient formula.

[ F(p) = p^2 + 5p ] [ F(q) = q^2 + 5q ]

Now, substitute these values into the expression:

[ \frac{F(p) - F(q)}{p - q} = \frac{(p^2 + 5p) - (q^2 + 5q)}{p - q} ]

Now, simplify the numerator:

[ = \frac{p^2 + 5p - q^2 - 5q}{p - q} ]

[ = \frac{p^2 - q^2 + 5(p - q)}{p - q} ]

[ = \frac{(p - q)(p + q) + 5(p - q)}{p - q} ]

[ = \frac{(p - q)(p + q + 5)}{p - q} ]

[ = p + q + 5 ]

Therefore, (\frac{F(p) - F(q)}{p - q} = p + q + 5).

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