7x/x^2+4x+9+1/x^2-9= eching

$$\frac { 7 x } { x ^ { 2 } + 4 x + 9 } + \frac { 1 } { x ^ { 2 } - 9 } =$$

Baholash

$$\frac{7x^{3}+x^{2}-59x+9}{\left(x^{2}-9\right)\left(x^{2}+4x+9\right)}$$

Qisqa yechim qadamlari

Faktor: x^{2}-9.

$$\frac{7x}{x^{2}+4x+9}+\frac{1}{\left(x-3\right)\left(x+3\right)}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2}+4x+9 va \left(x-3\right)\left(x+3\right) ning eng kichik umumiy karralisi \left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right). \frac{7x}{x^{2}+4x+9} ni \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)} marotabaga ko'paytirish. \frac{1}{\left(x-3\right)\left(x+3\right)} ni \frac{x^{2}+4x+9}{x^{2}+4x+9} marotabaga ko'paytirish.

$$\frac{7x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)}+\frac{x^{2}+4x+9}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)}$$

\frac{7x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)} va \frac{x^{2}+4x+9}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{7x\left(x-3\right)\left(x+3\right)+x^{2}+4x+9}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)}$$

7x\left(x-3\right)\left(x+3\right)+x^{2}+4x+9 ichidagi ko‘paytirishlarni bajaring.

$$\frac{7x^{3}+21x^{2}-21x^{2}-63x+x^{2}+4x+9}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)}$$

7x^{3}+21x^{2}-21x^{2}-63x+x^{2}+4x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{7x^{3}+x^{2}-59x+9}{\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right)}$$

\left(x-3\right)\left(x+3\right)\left(x^{2}+4x+9\right) ni kengaytirish.

$$\frac{7x^{3}+x^{2}-59x+9}{x^{4}+4x^{3}-36x-81}$$

x ga nisbatan hosilani topish

$$\frac{5103-162x-1845x^{2}-68x^{3}+173x^{4}-2x^{5}-7x^{6}}{\left(x^{2}-9\right)^{2}\left(x^{4}+8x^{3}+34x^{2}+72x+81\right)}$$