\title{Simple fraction II}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat}
\methods{ineq/addterm, ineq/mulexp, ineq/divexp, ineq/exsides
ineq/trans, ineq/addineq, ineq/mulineq}
\minsteps{4}

\text{x=random(a,b,c,d,p,q,r,s,t,u,v,x,y,z)}

\text{sh=shuffle(15)}
\integer{a=(item(1,\sh)+1)*random(-1,1)}
\integer{b=(item(2,\sh)+1)*random(-1,1)}
\integer{c=(item(3,\sh)+1)}

\matrix{data=>,<,1
<,>,-1
}
\text{data=randomrow(\data)}
\text{s1=item(1,\data)random(,=)}
\text{s2=item(2,\data)}
\integer{it=item(3,\data)}

\integer{d=-(\b)+(\it)*random(1..10)}
\function{left=(\x + \a)/(\x + \b)}
\real{tester=(\d+(\a))/(\d+(\b))}
\integer{c=\tester>1?1-\c:1+\c}
\text{s2=\tester>1?<:>}
\text{eqr=random(,=)}
\text{sign=\s2\eqr}
\text{ctx1=\x \s1 \d}
\text{ctx2=\left \sign \c}
\context{\ctx1
\ctx2}
\goal{contradiction}

\statement{
Prove that the inequality \(\left \sign \c) has no solution when
\(\x \s1 \d).
}


