4(1/x+9-1/x)+4(1/x+9-1/x)+4x(frac{-1}{(x+9)^2}+frac{1}{x^2}) eching

$$4 ( \frac { 1 } { x + 9 } - \frac { 1 } { x } ) + 4 ( \frac { 1 } { x + 9 } - \frac { 1 } { x } ) + 4 x ( \frac { - 1 } { ( x + 9 ) ^ { 2 } } + \frac { 1 } { x ^ { 2 } } )$$

Baholash

$$-\frac{324}{x\left(x+9\right)^{2}}$$

Qisqa yechim qadamlari

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

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

\frac{x}{x\left(x+9\right)} va \frac{x+9}{x\left(x+9\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x-\left(x+9\right) ichidagi ko‘paytirishlarni bajaring.

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

x-x-9 kabi iboralarga o‘xshab birlashtiring.

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

4\times \frac{-9}{x\left(x+9\right)} ni yagona kasrga aylantiring.

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

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

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

\frac{x}{x\left(x+9\right)} va \frac{x+9}{x\left(x+9\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x-\left(x+9\right) ichidagi ko‘paytirishlarni bajaring.

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

x-x-9 kabi iboralarga o‘xshab birlashtiring.

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

4\times \frac{-9}{x\left(x+9\right)} ni yagona kasrga aylantiring.

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

2\times \frac{4\left(-9\right)}{x\left(x+9\right)} ni olish uchun \frac{4\left(-9\right)}{x\left(x+9\right)} va \frac{4\left(-9\right)}{x\left(x+9\right)} ni birlashtirish.

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

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

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

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

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

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

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+x^{2}+18x+81}{x^{2}\left(x+9\right)^{2}}$$

-x^{2}+x^{2}+18x+81 kabi iboralarga o‘xshab birlashtiring.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}}$$

4\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}} ni yagona kasrga aylantiring.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

-36 hosil qilish uchun 4 va -9 ni ko'paytirish.

$$2\times \frac{-36}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

2\times \frac{-36}{x\left(x+9\right)} ni yagona kasrga aylantiring.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

4 ga 18x+81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x$$

\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x ni yagona kasrga aylantiring.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{\left(72x+324\right)x}{x^{2}\left(x+9\right)^{2}}$$

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x\left(x+9\right) va x\left(x+9\right)^{2} ning eng kichik umumiy karralisi x\left(x+9\right)^{2}. \frac{2\left(-36\right)}{x\left(x+9\right)} ni \frac{x+9}{x+9} marotabaga ko'paytirish.

$$\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} va \frac{72x+324}{x\left(x+9\right)^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(-36\right)\left(x+9\right)+72x+324}{x\left(x+9\right)^{2}}$$

2\left(-36\right)\left(x+9\right)+72x+324 ichidagi ko‘paytirishlarni bajaring.

$$\frac{-72x-648+72x+324}{x\left(x+9\right)^{2}}$$

-72x-648+72x+324 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-324}{x\left(x+9\right)^{2}}$$

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

$$\frac{-324}{x^{3}+18x^{2}+81x}$$

Kengaytirish

$$-\frac{324}{x\left(x+9\right)^{2}}$$

Qisqa yechim qadamlari

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

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

\frac{x}{x\left(x+9\right)} va \frac{x+9}{x\left(x+9\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x-\left(x+9\right) ichidagi ko‘paytirishlarni bajaring.

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

x-x-9 kabi iboralarga o‘xshab birlashtiring.

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

4\times \frac{-9}{x\left(x+9\right)} ni yagona kasrga aylantiring.

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

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

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

\frac{x}{x\left(x+9\right)} va \frac{x+9}{x\left(x+9\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x-\left(x+9\right) ichidagi ko‘paytirishlarni bajaring.

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

x-x-9 kabi iboralarga o‘xshab birlashtiring.

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

4\times \frac{-9}{x\left(x+9\right)} ni yagona kasrga aylantiring.

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

2\times \frac{4\left(-9\right)}{x\left(x+9\right)} ni olish uchun \frac{4\left(-9\right)}{x\left(x+9\right)} va \frac{4\left(-9\right)}{x\left(x+9\right)} ni birlashtirish.

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

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

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

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

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

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

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+x^{2}+18x+81}{x^{2}\left(x+9\right)^{2}}$$

-x^{2}+x^{2}+18x+81 kabi iboralarga o‘xshab birlashtiring.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}}$$

4\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}} ni yagona kasrga aylantiring.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

-36 hosil qilish uchun 4 va -9 ni ko'paytirish.

$$2\times \frac{-36}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

2\times \frac{-36}{x\left(x+9\right)} ni yagona kasrga aylantiring.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

4 ga 18x+81 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x$$

\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x ni yagona kasrga aylantiring.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{\left(72x+324\right)x}{x^{2}\left(x+9\right)^{2}}$$

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x\left(x+9\right) va x\left(x+9\right)^{2} ning eng kichik umumiy karralisi x\left(x+9\right)^{2}. \frac{2\left(-36\right)}{x\left(x+9\right)} ni \frac{x+9}{x+9} marotabaga ko'paytirish.

$$\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} va \frac{72x+324}{x\left(x+9\right)^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(-36\right)\left(x+9\right)+72x+324}{x\left(x+9\right)^{2}}$$

2\left(-36\right)\left(x+9\right)+72x+324 ichidagi ko‘paytirishlarni bajaring.

$$\frac{-72x-648+72x+324}{x\left(x+9\right)^{2}}$$

-72x-648+72x+324 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-324}{x\left(x+9\right)^{2}}$$

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

$$\frac{-324}{x^{3}+18x^{2}+81x}$$