Dziedzina

[ala1234]

Ustal dziedzine oraz skroc wyrazenie wymierne

a)

x^2+2xy+y^2
--------------- =
3x^2-3y^2

b)

x^2+2x-15
------------- =
2x-6

[agulka]

a)
\(D: x \neq y\)

\(\frac{x^2+2xy+y^2}{3x^2-3y^2} = \frac{(x+y)^2}{3(x+y)(x-y)} = \frac{x+y}{3(x-y)}\)

[irena]

a)
\(D:\ x \neq y\ \wedge \ x \neq -y\\D= \left\{(x,\ y):x \in R\ \wedge \ y \in R\ \wedge \ x \neq y\ \wedge x \neq -y \right\}\)

b)
\(\frac{x^2+2x-15}{2x-6}=\frac{(x-3)(x+5)}{2(x-3)}\\x-3 \neq 0\\D=R \setminus \left\{3 \right\} \\\frac{(x-3)(x+5)}{2(x-3)}=\frac{x+5}{2}\)