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

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

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. t-17 va t-11 ning eng kichik umumiy karralisi \left(t-17\right)\left(t-11\right). \frac{t-15}{t-17} ni \frac{t-11}{t-11} marotabaga ko'paytirish. \frac{t-9}{t-11} ni \frac{t-17}{t-17} marotabaga ko'paytirish.

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

\frac{\left(t-15\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)} va \frac{\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

\left(t-15\right)\left(t-11\right)-\left(t-9\right)\left(t-17\right) ichidagi ko‘paytirishlarni bajaring.

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

t^{2}-11t-15t+165-t^{2}+17t+9t-153 kabi iboralarga o‘xshab birlashtiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(t-17\right)\left(t-11\right) va t-5 ning eng kichik umumiy karralisi \left(t-17\right)\left(t-11\right)\left(t-5\right). \frac{12}{\left(t-17\right)\left(t-11\right)} ni \frac{t-5}{t-5} marotabaga ko'paytirish. \frac{t-3}{t-5} ni \frac{\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)} marotabaga ko'paytirish.

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

\frac{12\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} va \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)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

12\left(t-5\right)-\left(t-3\right)\left(t-17\right)\left(t-11\right) ichidagi ko‘paytirishlarni bajaring.

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

12t-60-t^{3}+28t^{2}-187t+3t^{2}-84t+561 kabi iboralarga o‘xshab birlashtiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(t-17\right)\left(t-11\right)\left(t-5\right) va t-3 ning eng kichik umumiy karralisi \left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right). \frac{-259t+501-t^{3}+31t^{2}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} ni \frac{t-3}{t-3} marotabaga ko'paytirish. \frac{t-7}{t-3} ni \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)} marotabaga ko'paytirish.

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

\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)} va \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)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

\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) ichidagi ko‘paytirishlarni bajaring.

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

-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 kabi iboralarga o‘xshab birlashtiring.

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

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

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

Kengaytirish

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. t-17 va t-11 ning eng kichik umumiy karralisi \left(t-17\right)\left(t-11\right). \frac{t-15}{t-17} ni \frac{t-11}{t-11} marotabaga ko'paytirish. \frac{t-9}{t-11} ni \frac{t-17}{t-17} marotabaga ko'paytirish.

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

\frac{\left(t-15\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)} va \frac{\left(t-9\right)\left(t-17\right)}{\left(t-17\right)\left(t-11\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

\left(t-15\right)\left(t-11\right)-\left(t-9\right)\left(t-17\right) ichidagi ko‘paytirishlarni bajaring.

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

t^{2}-11t-15t+165-t^{2}+17t+9t-153 kabi iboralarga o‘xshab birlashtiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(t-17\right)\left(t-11\right) va t-5 ning eng kichik umumiy karralisi \left(t-17\right)\left(t-11\right)\left(t-5\right). \frac{12}{\left(t-17\right)\left(t-11\right)} ni \frac{t-5}{t-5} marotabaga ko'paytirish. \frac{t-3}{t-5} ni \frac{\left(t-17\right)\left(t-11\right)}{\left(t-17\right)\left(t-11\right)} marotabaga ko'paytirish.

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

\frac{12\left(t-5\right)}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} va \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)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

12\left(t-5\right)-\left(t-3\right)\left(t-17\right)\left(t-11\right) ichidagi ko‘paytirishlarni bajaring.

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

12t-60-t^{3}+28t^{2}-187t+3t^{2}-84t+561 kabi iboralarga o‘xshab birlashtiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(t-17\right)\left(t-11\right)\left(t-5\right) va t-3 ning eng kichik umumiy karralisi \left(t-17\right)\left(t-11\right)\left(t-5\right)\left(t-3\right). \frac{-259t+501-t^{3}+31t^{2}}{\left(t-17\right)\left(t-11\right)\left(t-5\right)} ni \frac{t-3}{t-3} marotabaga ko'paytirish. \frac{t-7}{t-3} ni \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)} marotabaga ko'paytirish.

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

\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)} va \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)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

\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) ichidagi ko‘paytirishlarni bajaring.

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

-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 kabi iboralarga o‘xshab birlashtiring.

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

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

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