Evaluasi
\frac{2\left(x^{2}+1\right)}{x^{2}-1}
Luaskan
\frac{2\left(x^{2}+1\right)}{x^{2}-1}
Grafik
Bagikan
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\frac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari x-1 dan x+1 adalah \left(x-1\right)\left(x+1\right). Kalikan \frac{x+1}{x-1} kali \frac{x+1}{x+1}. Kalikan \frac{x-1}{x+1} kali \frac{x-1}{x-1}.
\frac{\left(x+1\right)\left(x+1\right)+\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Karena \frac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} dan \frac{\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.
\frac{x^{2}+x+x+1+x^{2}-x-x+1}{\left(x-1\right)\left(x+1\right)}
Kalikan bilangan berikut \left(x+1\right)\left(x+1\right)+\left(x-1\right)\left(x-1\right).
\frac{2x^{2}+2}{\left(x-1\right)\left(x+1\right)}
Gabungkan seperti suku di x^{2}+x+x+1+x^{2}-x-x+1.
\frac{2x^{2}+2}{x^{2}-1}
Luaskan \left(x-1\right)\left(x+1\right).
\frac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari x-1 dan x+1 adalah \left(x-1\right)\left(x+1\right). Kalikan \frac{x+1}{x-1} kali \frac{x+1}{x+1}. Kalikan \frac{x-1}{x+1} kali \frac{x-1}{x-1}.
\frac{\left(x+1\right)\left(x+1\right)+\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Karena \frac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} dan \frac{\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} memiliki penyebut yang sama, tambahkan bilangan dengan menambahkan pembilangnya.
\frac{x^{2}+x+x+1+x^{2}-x-x+1}{\left(x-1\right)\left(x+1\right)}
Kalikan bilangan berikut \left(x+1\right)\left(x+1\right)+\left(x-1\right)\left(x-1\right).
\frac{2x^{2}+2}{\left(x-1\right)\left(x+1\right)}
Gabungkan seperti suku di x^{2}+x+x+1+x^{2}-x-x+1.
\frac{2x^{2}+2}{x^{2}-1}
Luaskan \left(x-1\right)\left(x+1\right).
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