(2x+3/2x-3-2x-3/2x+3):24/4x^2-9 eching

$$( \frac { 2 x + 3 } { 2 x - 3 } - \frac { 2 x - 3 } { 2 x + 3 } ) : \frac { 24 } { 4 x ^ { 2 } - 9 }$$

Baholash

$$x$$

Qisqa yechim qadamlari

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

$$\frac{\frac{\left(2x+3\right)\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}-\frac{\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

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

$$\frac{\frac{\left(2x+3\right)\left(2x+3\right)-\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

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

$$\frac{\frac{4x^{2}+6x+6x+9-4x^{2}+6x+6x-9}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

4x^{2}+6x+6x+9-4x^{2}+6x+6x-9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{24x}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}}$$

\frac{24x}{\left(2x-3\right)\left(2x+3\right)} ni \frac{24}{4x^{2}-9} ga bo'lish \frac{24x}{\left(2x-3\right)\left(2x+3\right)} ga k'paytirish \frac{24}{4x^{2}-9} ga qaytarish.

$$\frac{24x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)\times 24}$$

Surat va maxrajdagi ikkala 24 ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala \left(2x-3\right)\left(2x+3\right) ni qisqartiring.

$$x$$

x ga nisbatan hosilani topish

$$1$$

Derivativ ifodasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{\left(2x+3\right)\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}-\frac{\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{\left(2x+3\right)\left(2x+3\right)-\left(2x-3\right)\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{4x^{2}+6x+6x+9-4x^{2}+6x+6x-9}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

4x^{2}+6x+6x+9-4x^{2}+6x+6x-9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{24x}{\left(2x-3\right)\left(2x+3\right)}}{\frac{24}{4x^{2}-9}})$$

\frac{24x}{\left(2x-3\right)\left(2x+3\right)} ni \frac{24}{4x^{2}-9} ga bo'lish \frac{24x}{\left(2x-3\right)\left(2x+3\right)} ga k'paytirish \frac{24}{4x^{2}-9} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)\times 24})$$

Surat va maxrajdagi ikkala 24 ni qisqartiring.

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

\frac{x\left(4x^{2}-9\right)}{\left(2x-3\right)\left(2x+3\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(2x-3\right)\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)})$$

Surat va maxrajdagi ikkala \left(2x-3\right)\left(2x+3\right) ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

ax^{n} hosilasi – nax^{n-1}.

$$x^{1-1}$$

1 dan 1 ni ayirish.

$$x^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$1$$