3/a-4+2/a+3-21/a^2-a-12 eching

$$\frac { 3 } { a - 4 } + \frac { 2 } { a + 3 } - \frac { 21 } { a ^ { 2 } - a - 12 }$$

Baholash

$$\frac{5}{a+3}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. a-4 va a+3 ning eng kichik umumiy karralisi \left(a-4\right)\left(a+3\right). \frac{3}{a-4} ni \frac{a+3}{a+3} marotabaga ko'paytirish. \frac{2}{a+3} ni \frac{a-4}{a-4} marotabaga ko'paytirish.

$$\frac{3\left(a+3\right)}{\left(a-4\right)\left(a+3\right)}+\frac{2\left(a-4\right)}{\left(a-4\right)\left(a+3\right)}-\frac{21}{a^{2}-a-12}$$

\frac{3\left(a+3\right)}{\left(a-4\right)\left(a+3\right)} va \frac{2\left(a-4\right)}{\left(a-4\right)\left(a+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3\left(a+3\right)+2\left(a-4\right)}{\left(a-4\right)\left(a+3\right)}-\frac{21}{a^{2}-a-12}$$

3\left(a+3\right)+2\left(a-4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3a+9+2a-8}{\left(a-4\right)\left(a+3\right)}-\frac{21}{a^{2}-a-12}$$

3a+9+2a-8 kabi iboralarga o‘xshab birlashtiring.

$$\frac{5a+1}{\left(a-4\right)\left(a+3\right)}-\frac{21}{a^{2}-a-12}$$

Faktor: a^{2}-a-12.

$$\frac{5a+1}{\left(a-4\right)\left(a+3\right)}-\frac{21}{\left(a-4\right)\left(a+3\right)}$$

\frac{5a+1}{\left(a-4\right)\left(a+3\right)} va \frac{21}{\left(a-4\right)\left(a+3\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5a+1-21}{\left(a-4\right)\left(a+3\right)}$$

5a+1-21 kabi iboralarga o‘xshab birlashtiring.

$$\frac{5a-20}{\left(a-4\right)\left(a+3\right)}$$

\frac{5a-20}{\left(a-4\right)\left(a+3\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{5\left(a-4\right)}{\left(a-4\right)\left(a+3\right)}$$

Surat va maxrajdagi ikkala a-4 ni qisqartiring.

$$\frac{5}{a+3}$$

a ga nisbatan hosilani topish

$$-\frac{5}{\left(a+3\right)^{2}}$$