Learn how to solve problems step by step online. (t)->(-1)lim((t^2+t)/((2t+1)^(1/3)+(t+2)^(1/3))). Faktorisieren Sie das Polynom t^2+t mit seinem größten gemeinsamen Faktor (GCF): t. Wenden Sie die Formel an: \lim_{x\to c}\left(\frac{a}{b}\right)=\lim_{x\to c}\left(\frac{a}{b}\frac{conjugate\left(b\right)}{conjugate\left(b\right)}\right), wobei a=t\left(t+1\right), b=\sqrt[3]{2t+1}+\sqrt[3]{t+2}, c=-1 und x=t. Wenden Sie die Formel an: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, wobei a=t\left(t+1\right), b=\sqrt[3]{2t+1}+\sqrt[3]{t+2}, c=\sqrt[3]{2t+1}-\sqrt[3]{t+2}, a/b=\frac{t\left(t+1\right)}{\sqrt[3]{2t+1}+\sqrt[3]{t+2}}, f=\sqrt[3]{2t+1}-\sqrt[3]{t+2}, c/f=\frac{\sqrt[3]{2t+1}-\sqrt[3]{t+2}}{\sqrt[3]{2t+1}-\sqrt[3]{t+2}} und a/bc/f=\frac{t\left(t+1\right)}{\sqrt[3]{2t+1}+\sqrt[3]{t+2}}\frac{\sqrt[3]{2t+1}-\sqrt[3]{t+2}}{\sqrt[3]{2t+1}-\sqrt[3]{t+2}}. Wenden Sie die Formel an: \left(a+b\right)\left(a+c\right)=a^2-b^2, wobei a=\sqrt[3]{2t+1}, b=\sqrt[3]{t+2}, c=-\sqrt[3]{t+2}, a+c=\sqrt[3]{2t+1}-\sqrt[3]{t+2} und a+b=\sqrt[3]{2t+1}+\sqrt[3]{t+2}.

(t)->(-1)lim((t^2+t)/((2t+1)^(1/3)+(t+2)^(1/3)))