(4/5-x+9/x-5)div(2/x+3/x-5) eching

$$( \frac { 4 } { 5 - x } + \frac { 9 } { x - 5 } ) \div ( \frac { 2 } { x } + \frac { 3 } { x - 5 } )$$

Baholash

$$\frac{x}{x-2}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5-x va x-5 ning eng kichik umumiy karralisi x-5. \frac{4}{5-x} ni \frac{-1}{-1} marotabaga ko'paytirish.

$$\frac{\frac{4\left(-1\right)}{x-5}+\frac{9}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

\frac{4\left(-1\right)}{x-5} va \frac{9}{x-5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{4\left(-1\right)+9}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

4\left(-1\right)+9 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{-4+9}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

-4+9 hisob-kitobini qiling.

$$\frac{\frac{5}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x-5 ning eng kichik umumiy karralisi x\left(x-5\right). \frac{2}{x} ni \frac{x-5}{x-5} marotabaga ko'paytirish. \frac{3}{x-5} ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{2\left(x-5\right)}{x\left(x-5\right)} va \frac{3x}{x\left(x-5\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

2\left(x-5\right)+3x ichidagi ko‘paytirishlarni bajaring.

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

2x-10+3x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{5}{x-5}}{\frac{5x-10}{x\left(x-5\right)}}$$

\frac{5}{x-5} ni \frac{5x-10}{x\left(x-5\right)} ga bo'lish \frac{5}{x-5} ga k'paytirish \frac{5x-10}{x\left(x-5\right)} ga qaytarish.

$$\frac{5x\left(x-5\right)}{\left(x-5\right)\left(5x-10\right)}$$

Surat va maxrajdagi ikkala x-5 ni qisqartiring.

$$\frac{5x}{5x-10}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{x}{x-2}$$

Kengaytirish

$$\frac{x}{x-2}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5-x va x-5 ning eng kichik umumiy karralisi x-5. \frac{4}{5-x} ni \frac{-1}{-1} marotabaga ko'paytirish.

$$\frac{\frac{4\left(-1\right)}{x-5}+\frac{9}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

\frac{4\left(-1\right)}{x-5} va \frac{9}{x-5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{4\left(-1\right)+9}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

4\left(-1\right)+9 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{-4+9}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

-4+9 hisob-kitobini qiling.

$$\frac{\frac{5}{x-5}}{\frac{2}{x}+\frac{3}{x-5}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x-5 ning eng kichik umumiy karralisi x\left(x-5\right). \frac{2}{x} ni \frac{x-5}{x-5} marotabaga ko'paytirish. \frac{3}{x-5} ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{2\left(x-5\right)}{x\left(x-5\right)} va \frac{3x}{x\left(x-5\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

2\left(x-5\right)+3x ichidagi ko‘paytirishlarni bajaring.

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

2x-10+3x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{5}{x-5}}{\frac{5x-10}{x\left(x-5\right)}}$$

\frac{5}{x-5} ni \frac{5x-10}{x\left(x-5\right)} ga bo'lish \frac{5}{x-5} ga k'paytirish \frac{5x-10}{x\left(x-5\right)} ga qaytarish.

$$\frac{5x\left(x-5\right)}{\left(x-5\right)\left(5x-10\right)}$$

Surat va maxrajdagi ikkala x-5 ni qisqartiring.

$$\frac{5x}{5x-10}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{x}{x-2}$$