(%i1) kill(all);

Result

1)ukol

(%i1) pom:x+y+1/(x+y);

Result

(%i2) ratsubst(z,x+y,%);

Result

(%i3) subst(z=x+y,%);

Result

(%i4) u:%;

Result

(%i5) partfrac(u,x);

Result

2)ukol

(%i6) pom:x^2+2*x+1+1/(x^2+2*x+1);

Result

(%i7) ratsubst(z,x^2+2*x+1,%);

Result

(%i8) subst(z=factor(x^2+2*x+1),%);

Result

(%i9) u:%;

Result

(%i10) z:partfrac(u,x);

Result

(%i11) expand(inpart(z,4))+z-inpart(z,4);

Result

(%i12) kill(all);

Result

3)ukol

(%i1) pom:((x+1)^10-2*y)/(x+y)^10+1/(x+y)^9-x/(x+y)^10;

Result

(%i2) subst(z,x+1,pom);

Result

(%i3) ratsimp(subst(w,x+y,%));

Result

(%i4) subst(w=x+y,%);

Result

(%i5) subst(z=x+1,%);

Result

(%i6) kill(all);

Result

4)ukol

(%i1) pol:(2*x^2+x)*(2*x^2-x);

Result

a

(%i2) factor(pol);

Result

(%i3) subst(x^2=z,%);

Result

(%i4) collectterms(expand(%),z);

Result

(%i5) subst(x^2,z,%);

Result

b)

(%i6) factor(pol);

Result

c)

(%i7) collectterms(expand(subst(z,2*x-1,factor(pol))),z);

Result

(%i8) subst(2*x-1,z,%);

Result

(%i9) kill(all);

Result

5)ukol

(%i1) pom:(x^2-a)/(x-sqrt(a));

Result

(%i2) subst(z^2,a,pom);

Result

(%i3) factor(%);

Result

(%i4) subst(sqrt(a),z,%);

Result


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