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

$$\frac { 3 } { a + b } + \frac { 2 } { a - b } - \frac { 1 } { a ^ { 2 } - b ^ { 2 } } =$$

Baholash

$$\frac{5a-b-1}{a^{2}-b^{2}}$$

Qisqa yechim qadamlari

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

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

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

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

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

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

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

$$\frac{5a-b}{\left(a+b\right)\left(a-b\right)}-\frac{1}{a^{2}-b^{2}}$$

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

$$\frac{5a-b}{\left(a+b\right)\left(a-b\right)}-\frac{1}{\left(a+b\right)\left(a-b\right)}$$

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

$$\frac{5a-b-1}{\left(a+b\right)\left(a-b\right)}$$

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

$$\frac{5a-b-1}{a^{2}-b^{2}}$$

a ga nisbatan hosilani topish

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