Slope: derivative of a pont on a curve

[morrowcosom]

Homework Statement

We are calculating the slope of the function f(x) = 1/x - x2 at x = 3/2.
For the function f(x) = 1/x - x2, we now know:

f(3/2) = -19/12
f(3/2+h) = (1)/(3/2 + h) - ((9/4) + 3h + h^2)
Now evaluate the difference quotient, simplifying as much as possible and cancelling h in the denominator:
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[f(3/2+h) - f(3/2)]h
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Homework Equations

3. The Attempt at a Solution
[(1)/(3/2 + h)) - ((9/4) + 3h + h^2) + (19/12)](1/h)
= ((12)/(3/2 + h)) - ((9/4) + 3h + h^2)+ ((19)/(3/2 + h)) - ((9/4) + 3h + h^2))/
((12)/(3/2 + h)) - ((9/4) + 3h + h^2))(1/h)

( I thought it would be a good idea to simplify the b term next)
=((12)/(18+12h)-(27+36h+12h^2)) + ((19)/(18+12h)-(27+36h+12h^2))/
((12)/(18+12h)-(27+36h+12h^2))(1/h)

=((12)/(18+12h)-(27+36h+12h^2)) + ((3/2)+h)((3/4)+h)/(18+12h)-(27+36h+12h^2))(1/h)
=12 + ((3/2)+h)-((3/4)+h/ (18+12h)-(27+36h+12h^2))(1/h) (cancel out the h's)

=(51/4)/ (18+12h)-(27+36h+12h^2)

I was doing independent study on a computer program and it says I was wrong. Where did I trip up?

 

[╔(σ_σ)╝]

Please consider using latex; your solution is not very readable.