\[\begin{align*}A\left( {t + h} \right) - A\left( t \right) & = \frac{{2t + 2h}}{{3 - t - h}} - \frac{{2t}}{{3 - t}}\\ & = \frac{{\left( {2t + 2h} \right)\left( {3 - t} \right) - 2t\left( {3 - t - h} \right)}}{{\left( {3 - t - h} \right)\left( {3 - t} \right)}}\\ & = \frac{{6t - 2{t^2} + 6h - 2ht - \left( {6t - 2{t^2} - 2th} \right)}}{{\left( {3 - t - h} \right)\left( {3 - t} \right)}}\\ & = \frac{{6h}}{{\left( {3 - t - h} \right)\left( {3 - t} \right)}}\end{align*}\]

E'tibor bering, farqli koeffitsientlar bilan ishlashda, keyingi bosqichga tayyorgarlik ko'rishda deyarli har doim ratsional iboralarni bitta atamaga birlashtirish tavsiya etiladi. Bundan tashqari, buni amalga oshirayotganda, suratni iloji boricha soddalashtirishni unutmang. Ko'p farqli koeffitsientlar bilan siz bu erda qilganimiz kabi juda ko'p bekor qilishni ko'rasiz.

\[\frac{{A\left( {t + h} \right) - A\left( t \right)}}{h} = \frac{1}{h}\left( {A\left( {t + h} \right) - A\left( t \right)} \right) = \frac{1}{h}\left( {\frac{{6h}}{{\left( {3 - t - h} \right)\left( {3 - t} \right)}}} \right) = \frac{6}{{\left( {3 - t - h} \right)\left( {3 - t} \right)}}\]

Ushbu bosqichda biz surat bilan ishlashni biroz osonlashtirish uchun farq koeffitsientini biroz qayta yozdik. Biz bu erda qilayotgan barcha narsa shundan iboratki,

\[\frac{a}{b} = \left( a \right)\left( {\frac{1}{b}} \right) = \left( {\frac{1}{b}} \right)\left( a \right)\]