5/2x^2-xy-3y^2+1/xy+y^2 eching

$$\frac { 5 } { 2 x ^ { 2 } - x y - 3 y ^ { 2 } } + \frac { 1 } { x y + y ^ { 2 } }$$

Baholash

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

Qisqa yechim qadamlari

Faktor: 2x^{2}-xy-3y^{2}. Faktor: xy+y^{2}.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+y\right)\left(2x-3y\right) va y\left(x+y\right) ning eng kichik umumiy karralisi y\left(x+y\right)\left(2x-3y\right). \frac{5}{\left(x+y\right)\left(2x-3y\right)} ni \frac{y}{y} marotabaga ko'paytirish. \frac{1}{y\left(x+y\right)} ni \frac{2x-3y}{2x-3y} marotabaga ko'paytirish.

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

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

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

5y+2x-3y kabi iboralarga o‘xshab birlashtiring.

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

\frac{2y+2x}{y\left(x+y\right)\left(2x-3y\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x+y ni qisqartiring.

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

y\left(2x-3y\right) ni kengaytirish.

$$\frac{2}{2xy-3y^{2}}$$

x ga nisbatan hosilani topish

$$-\frac{4}{y\left(2x-3y\right)^{2}}$$