Selesaikan t-15/t-17-t-9/t-11-t-3/t-5-t-7/t-3

$$\frac { t - 15 } { t - 17 } - \frac { t - 9 } { t - 11 } - \frac { t - 3 } { t - 5 } - \frac { t - 7 } { t - 3 }$$

Evaluasi

$$\frac{2\left(-t^{4}+37t^{3}-455t^{2}+2251t-4024\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Langkah-langkah Solusi Singkat

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari t-17 dan t-11 adalah \left(t-17\right)\left(t-11\right). Kalikan \frac{t-15}{t-17} kali \frac{t-11}{t-11}. Kalikan \frac{t-9}{t-11} kali \frac{t-17}{t-17}.

$$\frac{\left(t-15\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)}-\frac{\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Karena \frac{\left(t-15\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)} dan \frac{\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

$$\frac{\left(t-15\right)\left(t-11\right)-\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Kalikan bilangan berikut \left(t-15\right)\left(t-11\right)-\left(t-9\right)\left(t-17\right).

$$\frac{t^{2}-11t-15t+165-t^{2}+17t+9t-153}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Gabungkan seperti suku di t^{2}-11t-15t+165-t^{2}+17t+9t-153.

$$\frac{12}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari \left(t-17\right)\left(t-11\right) dan t-5 adalah \left(t-17\right)\left(t-11\right)\left(t-5\right). Kalikan \frac{12}{\left(t-17\right)\left(t-11\right)} kali \frac{t-5}{t-5}. Kalikan \frac{t-3}{t-5} kali \frac{\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)}.

$$\frac{12\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{\left(t-3\right)\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Karena \frac{12\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} dan \frac{\left(t-3\right)\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

$$\frac{12\left(t-5\right)-\left(t-3\right)\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Kalikan bilangan berikut 12\left(t-5\right)-\left(t-3\right)\left(t-17\right)\left(t-11\right).

$$\frac{12t-60-t^{3}+28t^{2}-187t+3t^{2}-84t+561}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Gabungkan seperti suku di 12t-60-t^{3}+28t^{2}-187t+3t^{2}-84t+561.

$$\frac{-259t+501-t^{3}+31t^{2}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari \left(t-17\right)\left(t-11\right)\left(t-5\right) dan t-3 adalah \left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right). Kalikan \frac{-259t+501-t^{3}+31t^{2}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} kali \frac{t-3}{t-3}. Kalikan \frac{t-7}{t-3} kali \frac{\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}.

$$\frac{\left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}-\frac{\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Karena \frac{\left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)} dan \frac{\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

$$\frac{\left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)-\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Kalikan bilangan berikut \left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)-\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right).

$$\frac{-259t^{2}+777t+501t-1503-t^{4}+3t^{3}+31t^{3}-93t^{2}-t^{4}+33t^{3}-327t^{2}+935t+7t^{3}-231t^{2}+2289t-6545}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Gabungkan seperti suku di -259t^{2}+777t+501t-1503-t^{4}+3t^{3}+31t^{3}-93t^{2}-t^{4}+33t^{3}-327t^{2}+935t+7t^{3}-231t^{2}+2289t-6545.

$$\frac{-910t^{2}+4502t-8048-2t^{4}+74t^{3}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Luaskan \left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right).

$$\frac{-910t^{2}+4502t-8048-2t^{4}+74t^{3}}{t^{4}-36t^{3}+426t^{2}-1916t+2805}$$

Luaskan

$$-\frac{2\left(t^{4}-37t^{3}+455t^{2}-2251t+4024\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Langkah-langkah Solusi Singkat

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari t-17 dan t-11 adalah \left(t-17\right)\left(t-11\right). Kalikan \frac{t-15}{t-17} kali \frac{t-11}{t-11}. Kalikan \frac{t-9}{t-11} kali \frac{t-17}{t-17}.

$$\frac{\left(t-15\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)}-\frac{\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Karena \frac{\left(t-15\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)} dan \frac{\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

$$\frac{\left(t-15\right)\left(t-11\right)-\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Kalikan bilangan berikut \left(t-15\right)\left(t-11\right)-\left(t-9\right)\left(t-17\right).

$$\frac{t^{2}-11t-15t+165-t^{2}+17t+9t-153}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Gabungkan seperti suku di t^{2}-11t-15t+165-t^{2}+17t+9t-153.

$$\frac{12}{\left(t-17\right)\left(t-11\right)}-\frac{t-3}{t-5}-\frac{t-7}{t-3}$$

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari \left(t-17\right)\left(t-11\right) dan t-5 adalah \left(t-17\right)\left(t-11\right)\left(t-5\right). Kalikan \frac{12}{\left(t-17\right)\left(t-11\right)} kali \frac{t-5}{t-5}. Kalikan \frac{t-3}{t-5} kali \frac{\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)}.

$$\frac{12\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{\left(t-3\right)\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Karena \frac{12\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} dan \frac{\left(t-3\right)\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

$$\frac{12\left(t-5\right)-\left(t-3\right)\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Kalikan bilangan berikut 12\left(t-5\right)-\left(t-3\right)\left(t-17\right)\left(t-11\right).

$$\frac{12t-60-t^{3}+28t^{2}-187t+3t^{2}-84t+561}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Gabungkan seperti suku di 12t-60-t^{3}+28t^{2}-187t+3t^{2}-84t+561.

$$\frac{-259t+501-t^{3}+31t^{2}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}-\frac{t-7}{t-3}$$

Untuk menambahkan atau mengurangi ekspresi, perluas untuk menyamakan penyebutnya. Kelipatan persekutuan terkecil dari \left(t-17\right)\left(t-11\right)\left(t-5\right) dan t-3 adalah \left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right). Kalikan \frac{-259t+501-t^{3}+31t^{2}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} kali \frac{t-3}{t-3}. Kalikan \frac{t-7}{t-3} kali \frac{\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)}.

$$\frac{\left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}-\frac{\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Karena \frac{\left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)} dan \frac{\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)} memiliki penyebut yang sama, kurangi bilangan dengan mengurangkan pembilangnya.

$$\frac{\left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)-\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Kalikan bilangan berikut \left(-259t+501-t^{3}+31t^{2}\right)\left(t-3\right)-\left(t-7\right)\left(t-17\right)\left(t-11\right)\left(t-5\right).

$$\frac{-259t^{2}+777t+501t-1503-t^{4}+3t^{3}+31t^{3}-93t^{2}-t^{4}+33t^{3}-327t^{2}+935t+7t^{3}-231t^{2}+2289t-6545}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Gabungkan seperti suku di -259t^{2}+777t+501t-1503-t^{4}+3t^{3}+31t^{3}-93t^{2}-t^{4}+33t^{3}-327t^{2}+935t+7t^{3}-231t^{2}+2289t-6545.

$$\frac{-910t^{2}+4502t-8048-2t^{4}+74t^{3}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right)}$$

Luaskan \left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right).

$$\frac{-910t^{2}+4502t-8048-2t^{4}+74t^{3}}{t^{4}-36t^{3}+426t^{2}-1916t+2805}$$