x^2/x^2+6x+9-4/x^2-9= eching

$$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 } - \frac { 4 } { x ^ { 2 } - 9 } =$$

Baholash

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

Qisqa yechim qadamlari

Faktor: x^{2}+6x+9. Faktor: x^{2}-9.

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

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

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

\frac{x^{2}\left(x-3\right)}{\left(x-3\right)\left(x+3\right)^{2}} va \frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

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

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

$$\frac{x^{3}-3x^{2}-4x-12}{x^{3}+3x^{2}-9x-27}$$

x ga nisbatan hosilani topish

$$\frac{2x\left(3x^{2}-14x+39\right)}{\left(x-3\right)^{2}\left(x+3\right)^{3}}$$