2/x^2+7x+10+3/x^2-25 eching

$$\frac { 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 } { x ^ { 2 } - 25 }$$

Baholash

$$\frac{5x-4}{\left(x+2\right)\left(x^{2}-25\right)}$$

Qisqa yechim qadamlari

Faktor: x^{2}+7x+10. Faktor: x^{2}-25.

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

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

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

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

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

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

$$\frac{2x-10+3x+6}{\left(x-5\right)\left(x+2\right)\left(x+5\right)}$$

2x-10+3x+6 kabi iboralarga o‘xshab birlashtiring.

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

\left(x-5\right)\left(x+2\right)\left(x+5\right) ni kengaytirish.

$$\frac{5x-4}{x^{3}+2x^{2}-25x-50}$$

x ga nisbatan hosilani topish

$$\frac{2\left(-5x^{3}+x^{2}+8x-175\right)}{\left(\left(x+2\right)\left(x^{2}-25\right)\right)^{2}}$$