Esercizio
$\frac{\frac{1}{\left(x+h\right)^2}-\frac{1}{x^2}}{h}$
Soluzione passo-passo
Impara online a risolvere i problemi di limiti all'infinito passo dopo passo. (1/((x+h)^2)+-1/(x^2))/h. Applicare la formula: a+\frac{b}{c}=\frac{b+ac}{c}, dove a=\frac{1}{\left(x+h\right)^2}, b=-1, c=x^2, a+b/c=\frac{1}{\left(x+h\right)^2}+\frac{-1}{x^2} e b/c=\frac{-1}{x^2}. Applicare la formula: a+\frac{b}{c}=\frac{b+ac}{c}, dove a=-1, b=x^2, c=\left(x+h\right)^2, a+b/c=-1+\frac{x^2}{\left(x+h\right)^2} e b/c=\frac{x^2}{\left(x+h\right)^2}. Applicare la formula: \frac{\frac{a}{b}}{c}=\frac{a}{bc}, dove a=\frac{x^2-\left(x+h\right)^2}{\left(x+h\right)^2}, b=x^2, c=h, a/b/c=\frac{\frac{\frac{x^2-\left(x+h\right)^2}{\left(x+h\right)^2}}{x^2}}{h} e a/b=\frac{\frac{x^2-\left(x+h\right)^2}{\left(x+h\right)^2}}{x^2}. Applicare la formula: \frac{\frac{a}{b}}{c}=\frac{a}{bc}, dove a=x^2-\left(x+h\right)^2, b=\left(x+h\right)^2, c=x^2h, a/b/c=\frac{\frac{x^2-\left(x+h\right)^2}{\left(x+h\right)^2}}{x^2h} e a/b=\frac{x^2-\left(x+h\right)^2}{\left(x+h\right)^2}.
Risposta finale al problema
$\frac{-2xh-h^{2}}{\left(x+h\right)^2x^2h}$