document.write( "Question 857700: if x+1/y=1 & y+1/z=1 then prove that z+1/x=1 \n" ); document.write( "

Algebra.Com's Answer #516762 by Fombitz(32388) $\"\"$ $\"About$

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1. $\"x%2B1%2Fy=1\"$
\n" ); document.write( "2. $\"y%2B1%2Fz=1\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"y=1-1%2Fz\"$
\n" ); document.write( " $\"y=%28z-1%29%2Fz\"$
\n" ); document.write( " $\"1%2Fy=z%2F%28z-1%29\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"x%2Bz%2F%28z-1%29=1\"$
\n" ); document.write( " $\"%28z-1%29x%2Bz=z-1\"$
\n" ); document.write( " $\"zx-x%2Bz=z-1\"$
\n" ); document.write( " $\"zx-x=-1\"$
\n" ); document.write( " $\"zx=-1%2Bx\"$
\n" ); document.write( " $\"z=%28x-1%29%2Fx\"$
\n" ); document.write( " $\"z=1-1%2Fx\"$
\n" ); document.write( " $\"z%2B1%2Fx=1\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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