x/4x^2-12x+9-3x/9-4x^2 eching

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

Baholash

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

Qisqa yechim qadamlari

Faktor: 4x^{2}-12x+9. Faktor: 9-4x^{2}.

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

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

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

\frac{x\left(2x+3\right)}{\left(2x+3\right)\left(2x-3\right)^{2}} va \frac{3x\left(-1\right)\left(2x-3\right)}{\left(2x+3\right)\left(2x-3\right)^{2}} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x\left(2x+3\right)-3x\left(-1\right)\left(2x-3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x^{2}+3x+6x^{2}-9x}{\left(2x+3\right)\left(2x-3\right)^{2}}$$

2x^{2}+3x+6x^{2}-9x kabi iboralarga o‘xshab birlashtiring.

$$\frac{8x^{2}-6x}{\left(2x+3\right)\left(2x-3\right)^{2}}$$

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

$$\frac{8x^{2}-6x}{8x^{3}-12x^{2}-18x+27}$$

Omil

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