Proszę o pomoc nad tymi działaniami :) Wykonaj działanie a) [latex]frac{ x^{2}+y^{2}}{x^{2}-y^{2}} - frac{x+y}{2x-2y} + 1=[/latex] b) [latex]frac{1}{a-b}- frac{3ab}{a^{3}-b^{3}}-frac{b-a}{a^{2}+ab+b^{2}} =[/latex]

[latex]\frac{x^2+y^2}{(x+y)(x-y)}-frac{x+y}{2(x-y)}+1=frac{2(x^2+y^2)-(x+y)^2+2(x^2-y^2)}{2(x+y)(x-y)}= \ \frac{2x^2+2y^2-x^2-2xy-y^2+2x^2-2y^2}{2(x+y)(x-y)}=frac{3x^2-y^2-2xy}{2(x+y)(x-y)}= \ \frac{3x^2+xy-3xy-y^2}{2(x+y)(x-y)}=frac{x(3x+y)-y(3x+y)}{2(x+y)(x-y)}=frac{(3x+y)(x-y)}{2(x+y)(x-y)}=frac{3x+y}{2x+2y} \ \x eq y, x eq-y \ \frac{1}{a-b}-frac{3ab}{(a-b)(a^2+ab+b^2)}-frac{b-a}{a^2+ab+b^2}=frac{a^2+ab+b^2-3ab+(a-b)^2}{(a-b)(a^2+ab+b^2)}= [/latex] [latex]\frac{a^2+ab+b^2-3ab+a^2-2ab+b^2}{(a-b)(a^2+ab+b^2)}=frac{2a^2+2b^2-4ab}{(a-b)(a^2+ab+b^2)}= \ \frac{2(a^2-2ab+b^2)}{(a-b)(a^2+ab+b^2)}=frac{2(a-b)^2}{(a-b)(a^2+ab+b^2)}=frac{2(a-b)}{a^2+ab+b^2}=frac{2a-2b}{a^2+ab+b^2} \ \a eq b[/latex]