1/k-r+4r/k^2-r^2+2/k+r eching

$$\frac { 1 } { k - r } + \frac { 4 r } { k ^ { 2 } - r ^ { 2 } } + \frac { 2 } { k + r }$$

Baholash

$$\frac{3}{k-r}$$

Qisqa yechim qadamlari

Faktor: k^{2}-r^{2}.

$$\frac{1}{k-r}+\frac{4r}{\left(r+k\right)\left(-r+k\right)}+\frac{2}{k+r}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. k-r va \left(r+k\right)\left(-r+k\right) ning eng kichik umumiy karralisi \left(r+k\right)\left(-r+k\right). \frac{1}{k-r} ni \frac{r+k}{r+k} marotabaga ko'paytirish.

$$\frac{r+k}{\left(r+k\right)\left(-r+k\right)}+\frac{4r}{\left(r+k\right)\left(-r+k\right)}+\frac{2}{k+r}$$

\frac{r+k}{\left(r+k\right)\left(-r+k\right)} va \frac{4r}{\left(r+k\right)\left(-r+k\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{r+k+4r}{\left(r+k\right)\left(-r+k\right)}+\frac{2}{k+r}$$

r+k+4r kabi iboralarga o‘xshab birlashtiring.

$$\frac{5r+k}{\left(r+k\right)\left(-r+k\right)}+\frac{2}{k+r}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(r+k\right)\left(-r+k\right) va k+r ning eng kichik umumiy karralisi \left(r+k\right)\left(-r+k\right). \frac{2}{k+r} ni \frac{-r+k}{-r+k} marotabaga ko'paytirish.

$$\frac{5r+k}{\left(r+k\right)\left(-r+k\right)}+\frac{2\left(-r+k\right)}{\left(r+k\right)\left(-r+k\right)}$$

\frac{5r+k}{\left(r+k\right)\left(-r+k\right)} va \frac{2\left(-r+k\right)}{\left(r+k\right)\left(-r+k\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5r+k+2\left(-r+k\right)}{\left(r+k\right)\left(-r+k\right)}$$

5r+k+2\left(-r+k\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{5r+k-2r+2k}{\left(r+k\right)\left(-r+k\right)}$$

5r+k-2r+2k kabi iboralarga o‘xshab birlashtiring.

$$\frac{3r+3k}{\left(r+k\right)\left(-r+k\right)}$$

\frac{3r+3k}{\left(r+k\right)\left(-r+k\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{3\left(r+k\right)}{\left(r+k\right)\left(-r+k\right)}$$

Surat va maxrajdagi ikkala r+k ni qisqartiring.

$$\frac{3}{-r+k}$$

k ga nisbatan hosilani topish

$$-\frac{3}{\left(k-r\right)^{2}}$$