Nilaikan
\frac{\alpha ^{2}+\alpha +\beta ^{2}+\beta }{\left(\alpha +1\right)\left(\beta +1\right)}
Bezakan w.r.t. α
\frac{\alpha ^{2}+2\alpha -\beta ^{2}-\beta +1}{\left(\beta +1\right)\left(\alpha +1\right)^{2}}
Kongsi
Disalin ke papan klip
\frac{\alpha \left(\alpha +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}+\frac{\beta \left(\beta +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}
Untuk menambah atau menolak ungkapan, kembangkannya untuk membuat penyebut mereka sama. Gandaan sepunya terkecil \beta +1 dan \alpha +1 ialah \left(\alpha +1\right)\left(\beta +1\right). Darabkan \frac{\alpha }{\beta +1} kali \frac{\alpha +1}{\alpha +1}. Darabkan \frac{\beta }{\alpha +1} kali \frac{\beta +1}{\beta +1}.
\frac{\alpha \left(\alpha +1\right)+\beta \left(\beta +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}
Oleh kerana \frac{\alpha \left(\alpha +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)} dan \frac{\beta \left(\beta +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)} mempunyai penyebut yang sama, tambahkan dengan menambahkan pengangka.
\frac{\alpha ^{2}+\alpha +\beta ^{2}+\beta }{\left(\alpha +1\right)\left(\beta +1\right)}
Lakukan pendaraban dalam \alpha \left(\alpha +1\right)+\beta \left(\beta +1\right).
\frac{\alpha ^{2}+\alpha +\beta ^{2}+\beta }{\alpha \beta +\alpha +\beta +1}
Kembangkan \left(\alpha +1\right)\left(\beta +1\right).
Contoh
Persamaan kuadratik
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometri
4 \sin \theta \cos \theta = 2 \sin \theta
Persamaan linear
y = 3x + 4
Aritmetik
699 * 533
Matriks
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Persamaan serentak
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Pembezaan
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Pengamiran
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Had
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}