3x+5/x-4-7x^2+38x+59/3x^2-5x-28+x+1/3x+7 eching

$$\frac { 3 x + 5 } { x - 4 } - \frac { 7 x ^ { 2 } + 38 x + 59 } { 3 x ^ { 2 } - 5 x - 28 } + \frac { x + 1 } { 3 x + 7 }$$

Baholash

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Qisqa yechim qadamlari

Faktor: 3x^{2}-5x-28.

$$\frac{3x+5}{x-4}-\frac{7x^{2}+38x+59}{\left(x-4\right)\left(3x+7\right)}+\frac{x+1}{3x+7}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-4 va \left(x-4\right)\left(3x+7\right) ning eng kichik umumiy karralisi \left(x-4\right)\left(3x+7\right). \frac{3x+5}{x-4} ni \frac{3x+7}{3x+7} marotabaga ko'paytirish.

$$\frac{\left(3x+5\right)\left(3x+7\right)}{\left(x-4\right)\left(3x+7\right)}-\frac{7x^{2}+38x+59}{\left(x-4\right)\left(3x+7\right)}+\frac{x+1}{3x+7}$$

\frac{\left(3x+5\right)\left(3x+7\right)}{\left(x-4\right)\left(3x+7\right)} va \frac{7x^{2}+38x+59}{\left(x-4\right)\left(3x+7\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(3x+5\right)\left(3x+7\right)-\left(7x^{2}+38x+59\right)}{\left(x-4\right)\left(3x+7\right)}+\frac{x+1}{3x+7}$$

\left(3x+5\right)\left(3x+7\right)-\left(7x^{2}+38x+59\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{9x^{2}+21x+15x+35-7x^{2}-38x-59}{\left(x-4\right)\left(3x+7\right)}+\frac{x+1}{3x+7}$$

9x^{2}+21x+15x+35-7x^{2}-38x-59 kabi iboralarga o‘xshab birlashtiring.

$$\frac{2x^{2}-2x-24}{\left(x-4\right)\left(3x+7\right)}+\frac{x+1}{3x+7}$$

\frac{2x^{2}-2x-24}{\left(x-4\right)\left(3x+7\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{2\left(x-4\right)\left(x+3\right)}{\left(x-4\right)\left(3x+7\right)}+\frac{x+1}{3x+7}$$

Surat va maxrajdagi ikkala x-4 ni qisqartiring.

$$\frac{2\left(x+3\right)}{3x+7}+\frac{x+1}{3x+7}$$

\frac{2\left(x+3\right)}{3x+7} va \frac{x+1}{3x+7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(x+3\right)+x+1}{3x+7}$$

2\left(x+3\right)+x+1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x+6+x+1}{3x+7}$$

2x+6+x+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3x+7}{3x+7}$$

Surat va maxrajdagi ikkala 3x+7 ni qisqartiring.

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Omil

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