a+1/a^2-a-a-1/a^2+a-1/a^2-1 eching

$$\frac { a + 1 } { a ^ { 2 } - a } - \frac { a - 1 } { a ^ { 2 } + a } - \frac { 1 } { a ^ { 2 } - 1 }$$

Baholash

$$\frac{3}{a^{2}-1}$$

Qisqa yechim qadamlari

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

$$\frac{a+1}{a\left(a-1\right)}-\frac{a-1}{a\left(a+1\right)}-\frac{1}{a^{2}-1}$$

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

$$\frac{\left(a+1\right)\left(a+1\right)}{a\left(a-1\right)\left(a+1\right)}-\frac{\left(a-1\right)\left(a-1\right)}{a\left(a-1\right)\left(a+1\right)}-\frac{1}{a^{2}-1}$$

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

$$\frac{\left(a+1\right)\left(a+1\right)-\left(a-1\right)\left(a-1\right)}{a\left(a-1\right)\left(a+1\right)}-\frac{1}{a^{2}-1}$$

\left(a+1\right)\left(a+1\right)-\left(a-1\right)\left(a-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{a^{2}+a+a+1-a^{2}+a+a-1}{a\left(a-1\right)\left(a+1\right)}-\frac{1}{a^{2}-1}$$

a^{2}+a+a+1-a^{2}+a+a-1 kabi iboralarga o‘xshab birlashtiring.

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

Surat va maxrajdagi ikkala a ni qisqartiring.

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

Faktor: a^{2}-1.

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

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

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

\left(a-1\right)\left(a+1\right) ni kengaytirish.

$$\frac{3}{a^{2}-1}$$

Kengaytirish

$$\frac{3}{a^{2}-1}$$

Qisqa yechim qadamlari

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

$$\frac{a+1}{a\left(a-1\right)}-\frac{a-1}{a\left(a+1\right)}-\frac{1}{a^{2}-1}$$

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

$$\frac{\left(a+1\right)\left(a+1\right)}{a\left(a-1\right)\left(a+1\right)}-\frac{\left(a-1\right)\left(a-1\right)}{a\left(a-1\right)\left(a+1\right)}-\frac{1}{a^{2}-1}$$

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

$$\frac{\left(a+1\right)\left(a+1\right)-\left(a-1\right)\left(a-1\right)}{a\left(a-1\right)\left(a+1\right)}-\frac{1}{a^{2}-1}$$

\left(a+1\right)\left(a+1\right)-\left(a-1\right)\left(a-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{a^{2}+a+a+1-a^{2}+a+a-1}{a\left(a-1\right)\left(a+1\right)}-\frac{1}{a^{2}-1}$$

a^{2}+a+a+1-a^{2}+a+a-1 kabi iboralarga o‘xshab birlashtiring.

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

Surat va maxrajdagi ikkala a ni qisqartiring.

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

Faktor: a^{2}-1.

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

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

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

\left(a-1\right)\left(a+1\right) ni kengaytirish.

$$\frac{3}{a^{2}-1}$$