x^2+x/x^2-25+x^2-1/x^2+11x+30 eching

$$\frac { x ^ { 2 } + x } { x ^ { 2 } - 25 } + \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 11 x + 30 }$$

Baholash

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

Qisqa yechim qadamlari

Faktor: x^{2}-25. Faktor: x^{2}+11x+30.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-5\right)\left(x+5\right) va \left(x+5\right)\left(x+6\right) ning eng kichik umumiy karralisi \left(x-5\right)\left(x+5\right)\left(x+6\right). \frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)} ni \frac{x+6}{x+6} marotabaga ko'paytirish. \frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)} ni \frac{x-5}{x-5} marotabaga ko'paytirish.

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

\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} va \frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right) ichidagi ko‘paytirishlarni bajaring.

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

x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5 kabi iboralarga o‘xshab birlashtiring.

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

\left(x-5\right)\left(x+5\right)\left(x+6\right) ni kengaytirish.

$$\frac{2x^{3}+2x^{2}+5x+5}{x^{3}+6x^{2}-25x-150}$$

Kengaytirish

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x+6\right)\left(x^{2}-25\right)}$$

Qisqa yechim qadamlari

Faktor: x^{2}-25. Faktor: x^{2}+11x+30.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-5\right)\left(x+5\right) va \left(x+5\right)\left(x+6\right) ning eng kichik umumiy karralisi \left(x-5\right)\left(x+5\right)\left(x+6\right). \frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)} ni \frac{x+6}{x+6} marotabaga ko'paytirish. \frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)} ni \frac{x-5}{x-5} marotabaga ko'paytirish.

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

\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} va \frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right) ichidagi ko‘paytirishlarni bajaring.

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

x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5 kabi iboralarga o‘xshab birlashtiring.

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

\left(x-5\right)\left(x+5\right)\left(x+6\right) ni kengaytirish.

$$\frac{2x^{3}+2x^{2}+5x+5}{x^{3}+6x^{2}-25x-150}$$