Question: A meteorologist uses a function $ f(h) = rac{2h^2 - 5h + 3}{h - 1} $ to model rainfall intensity $ f(h) $ (in mm/h) at hour $ h $ after a storm front begins. Simplify $ f(h) $ and compute $ \lim_{h o 1} f(h) $.

["Understanding Rainfall Intensity: Simplifying the Meteorological Model", "When analyzing rainfall patterns after a storm front passes, meteorologists often rely on precise mathematical models. One such model uses the function\n[ f(h) = \frac{2h^2 - 5h + 3}{h - 1} ]\nto describe rainfall intensity in millimeters per hour $ f(h) $ at hour $ h $ following the storm’s arrival. To better evaluate behavior near $ h = 1 $, such as peak intensity or interpolation, it is essential to simplify the expression and compute the limit as $ h $ approaches 1.", "---", "### Step 1: Factor the Numerator", "Start by factoring the quadratic in the numerator:\n[ 2h^2 - 5h + 3 ]", "We seek two numbers that multiply to $ 2 \ imes 3 = 6 $ and add to $ -5 $. These numbers are $ -2 $ and $ -3 $. Rewrite the middle term:\n[ 2h^2 - 2h - 3h + 3 ]\nGroup terms:\n[ (2h^2 - 2h) - (3h - 3) = 2h(h - 1) - 3(h - 1) = (2h - 3)(h - 1) ]", "So,\n[ f(h) = \frac{(2h - 3)(h - 1)}{h - 1} ]", "---", "### Step 2: Simplify the Expression", "For $ h <br/>\ne 1 $, the $ h - 1 $ terms cancel:\n[ f(h) = 2h - 3 \quad \ ext{for } h <br/>\ne 1 ]", "Although $ f(h) $ is undefined at $ h = 1 $ due to division by zero, the simplified form $ f(h) = 2h - 3 $ provides insight for limits.", "---", "### Step 3: Compute the Limit as $ h \ o 1 $", "Now compute:\n[ \lim_{h \ o 1} f(h) = \lim_{h \ o 1} (2h - 3) = 2(1) - 3 = -1 ]", "Thus, even though the function has a removable discontinuity at $ h = 1 $, the limiting rainfall intensity approaches $-1$ mm/h. Meteorologists interpret this as approaching 1 mm/h of decreasing or reversing rainfall immediately after the peak, consistent with early clearing conditions.", "---", "### Conclusion", "By factoring and simplifying, meteorologists can evaluate critical transition points in storm dynamics. The function $ f(h) $ simplifies to $ 2h - 3 $ for $ h <br/>\ne 1 $, and the limit as $ h $ approaches 1 is $-1$, indicating a bounded, predictable decline in rainfall intensity near the storm’s peak influence.", "Keywords: meteorologist, rainfall model, function simplification, limit as $ h \ o 1 $, storm intensity, $ f(h) = \frac{2h^2 - 5h + 3}{h - 1} $, limit computation, data analysis in meteorology."]