frac{x^{2}-8x+15}{5x^2+10x}divx^2-9/10x^2*x^2+5x+6/2x-10 eching

$$\frac { x ^ { 2 } - 8 x + 15 } { 5 x ^ { 2 } + 10 x } \div \frac { x ^ { 2 } - 9 } { 10 x ^ { 2 } } \times \frac { x ^ { 2 } + 5 x + 6 } { 2 x - 10 }$$

Baholash

$$x$$

Qisqa yechim qadamlari

\frac{x^{2}-8x+15}{5x^{2}+10x} ni \frac{x^{2}-9}{10x^{2}} ga bo'lish \frac{x^{2}-8x+15}{5x^{2}+10x} ga k'paytirish \frac{x^{2}-9}{10x^{2}} ga qaytarish.

$$\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)}\times \frac{x^{2}+5x+6}{2x-10}$$

\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{10\left(x-5\right)\left(x-3\right)x^{2}}{5x\left(x-3\right)\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10}$$

Surat va maxrajdagi ikkala 5x\left(x-3\right) ni qisqartiring.

$$\frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)} ni \frac{x^{2}+5x+6}{2x-10} ga ko‘paytiring.

$$\frac{2x\left(x-5\right)\left(x^{2}+5x+6\right)}{\left(x+2\right)\left(x+3\right)\left(2x-10\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{2x\left(x-5\right)\left(x+2\right)\left(x+3\right)}{2\left(x-5\right)\left(x+2\right)\left(x+3\right)}$$

Surat va maxrajdagi ikkala 2\left(x-5\right)\left(x+2\right)\left(x+3\right) ni qisqartiring.

$$x$$

x ga nisbatan hosilani topish

$$1$$

Derivativ ifodasidan foydalanish qadamlari

\frac{x^{2}-8x+15}{5x^{2}+10x} ni \frac{x^{2}-9}{10x^{2}} ga bo'lish \frac{x^{2}-8x+15}{5x^{2}+10x} ga k'paytirish \frac{x^{2}-9}{10x^{2}} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)}\times \frac{x^{2}+5x+6}{2x-10})$$

\frac{\left(x^{2}-8x+15\right)\times 10x^{2}}{\left(5x^{2}+10x\right)\left(x^{2}-9\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10\left(x-5\right)\left(x-3\right)x^{2}}{5x\left(x-3\right)\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10})$$

Surat va maxrajdagi ikkala 5x\left(x-3\right) ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}+5x+6}{2x-10})$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2x\left(x-5\right)}{\left(x+2\right)\left(x+3\right)} ni \frac{x^{2}+5x+6}{2x-10} ga ko‘paytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-5\right)\left(x^{2}+5x+6\right)}{\left(x+2\right)\left(x+3\right)\left(2x-10\right)})$$

\frac{2x\left(x-5\right)\left(x^{2}+5x+6\right)}{\left(x+2\right)\left(x+3\right)\left(2x-10\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x\left(x-5\right)\left(x+2\right)\left(x+3\right)}{2\left(x-5\right)\left(x+2\right)\left(x+3\right)})$$

Surat va maxrajdagi ikkala 2\left(x-5\right)\left(x+2\right)\left(x+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.

$$1$$