6x^-1-5y^-1/36x^-2-25y^-2 eching

$$\frac { 6 x ^ { - 1 } - 5 y ^ { - 1 } } { 36 x ^ { - 2 } - 25 y ^ { - 2 } }$$

Baholash

$$\frac{xy}{5x+6y}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(-5\times \frac{1}{y}x+6\right)\times \frac{1}{x}}{\left(-25y^{-2}x^{2}+36\right)x^{-2}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\left(-5\times \frac{1}{y}x+6\right)x^{1}}{-25y^{-2}x^{2}+36}$$

Ifodani kengaytiring.

$$\frac{-5\times \frac{1}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

-5\times \frac{1}{y} ni yagona kasrga aylantiring.

$$\frac{\frac{-5}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

\frac{-5}{y}x^{2} ni yagona kasrga aylantiring.

$$\frac{\frac{-5x^{2}}{y}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 6x ni \frac{y}{y} marotabaga ko'paytirish.

$$\frac{\frac{-5x^{2}}{y}+\frac{6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

\frac{-5x^{2}}{y} va \frac{6xy}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

\frac{1}{y}x ni yagona kasrga aylantiring.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{x}{y}\right)^{2}}$$

\frac{x}{y}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \frac{x^{2}}{y^{2}}}$$

-25\times \frac{x^{2}}{y^{2}} ni yagona kasrga aylantiring.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36+\frac{-25x^{2}}{y^{2}}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 36 ni \frac{y^{2}}{y^{2}} marotabaga ko'paytirish.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}}{y^{2}}+\frac{-25x^{2}}{y^{2}}}$$

\frac{36y^{2}}{y^{2}} va \frac{-25x^{2}}{y^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}-25x^{2}}{y^{2}}}$$

\frac{-5x^{2}+6xy}{y} ni \frac{36y^{2}-25x^{2}}{y^{2}} ga bo'lish \frac{-5x^{2}+6xy}{y} ga k'paytirish \frac{36y^{2}-25x^{2}}{y^{2}} ga qaytarish.

$$\frac{\left(-5x^{2}+6xy\right)y^{2}}{y\left(36y^{2}-25x^{2}\right)}$$

Surat va maxrajdagi ikkala y ni qisqartiring.

$$\frac{y\left(-5x^{2}+6xy\right)}{-25x^{2}+36y^{2}}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{xy\left(-5x+6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

-5x+6y mislodagi manfiy ishorani chiqarib tashlang.

$$\frac{-xy\left(5x-6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

Surat va maxrajdagi ikkala 5x-6y ni qisqartiring.

$$\frac{-xy}{-5x-6y}$$

Kengaytirish

$$\frac{xy}{5x+6y}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(-5\times \frac{1}{y}x+6\right)\times \frac{1}{x}}{\left(-25y^{-2}x^{2}+36\right)x^{-2}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\left(-5\times \frac{1}{y}x+6\right)x^{1}}{-25y^{-2}x^{2}+36}$$

Ifodani kengaytiring.

$$\frac{-5\times \frac{1}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

-5\times \frac{1}{y} ni yagona kasrga aylantiring.

$$\frac{\frac{-5}{y}x^{2}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

\frac{-5}{y}x^{2} ni yagona kasrga aylantiring.

$$\frac{\frac{-5x^{2}}{y}+6x}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 6x ni \frac{y}{y} marotabaga ko'paytirish.

$$\frac{\frac{-5x^{2}}{y}+\frac{6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

\frac{-5x^{2}}{y} va \frac{6xy}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{1}{y}x\right)^{2}}$$

\frac{1}{y}x ni yagona kasrga aylantiring.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \left(\frac{x}{y}\right)^{2}}$$

\frac{x}{y}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36-25\times \frac{x^{2}}{y^{2}}}$$

-25\times \frac{x^{2}}{y^{2}} ni yagona kasrga aylantiring.

$$\frac{\frac{-5x^{2}+6xy}{y}}{36+\frac{-25x^{2}}{y^{2}}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 36 ni \frac{y^{2}}{y^{2}} marotabaga ko'paytirish.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}}{y^{2}}+\frac{-25x^{2}}{y^{2}}}$$

\frac{36y^{2}}{y^{2}} va \frac{-25x^{2}}{y^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{-5x^{2}+6xy}{y}}{\frac{36y^{2}-25x^{2}}{y^{2}}}$$

\frac{-5x^{2}+6xy}{y} ni \frac{36y^{2}-25x^{2}}{y^{2}} ga bo'lish \frac{-5x^{2}+6xy}{y} ga k'paytirish \frac{36y^{2}-25x^{2}}{y^{2}} ga qaytarish.

$$\frac{\left(-5x^{2}+6xy\right)y^{2}}{y\left(36y^{2}-25x^{2}\right)}$$

Surat va maxrajdagi ikkala y ni qisqartiring.

$$\frac{y\left(-5x^{2}+6xy\right)}{-25x^{2}+36y^{2}}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{xy\left(-5x+6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

-5x+6y mislodagi manfiy ishorani chiqarib tashlang.

$$\frac{-xy\left(5x-6y\right)}{\left(-5x-6y\right)\left(5x-6y\right)}$$

Surat va maxrajdagi ikkala 5x-6y ni qisqartiring.

$$\frac{-xy}{-5x-6y}$$