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

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

Baholash

$$\frac{2a}{1-a^{4}}$$

Qisqa yechim qadamlari

Faktor: 1-a^{2}.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(a-1\right)\left(-a-1\right) va 1+a^{2} ning eng kichik umumiy karralisi \left(a-1\right)\left(-a-1\right)\left(a^{2}+1\right). \frac{a}{\left(a-1\right)\left(-a-1\right)} ni \frac{a^{2}+1}{a^{2}+1} marotabaga ko'paytirish. \frac{a}{1+a^{2}} ni \frac{\left(a-1\right)\left(-a-1\right)}{\left(a-1\right)\left(-a-1\right)} marotabaga ko'paytirish.

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

\frac{a\left(a^{2}+1\right)}{\left(a-1\right)\left(-a-1\right)\left(a^{2}+1\right)} va \frac{a\left(a-1\right)\left(-a-1\right)}{\left(a-1\right)\left(-a-1\right)\left(a^{2}+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

a\left(a^{2}+1\right)+a\left(a-1\right)\left(-a-1\right) ichidagi ko‘paytirishlarni bajaring.

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

a^{3}+a-a^{3}-a^{2}+a^{2}+a kabi iboralarga o‘xshab birlashtiring.

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

\left(a-1\right)\left(-a-1\right)\left(a^{2}+1\right) ni kengaytirish.

$$\frac{2a}{-a^{4}+1}$$

Omil

$$\frac{2a}{1-a^{4}}$$