Question 1049097
Both must be true:
(1) {{{ -( x + 1/z ) = 2 }}}
(2) {{{ x + 1/z = 2 }}}
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add (1) and (2)
(1) {{{ x + 1/z = -2 }}}
(2) {{{ x + 1/z = 2 }}}
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(1) {{{ 1/z = -x - 2 }}}
(2) {{{ 1/z = -x + 2 }}}
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(1) {{{ z = -1/( x + 2 ) }}}
(2) {{{ z = -1/( x - 2 ) }}}
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Here are plots of these relations:
{{{ graph( 400, 400, -10, 10, -10, 10, -1/( x+2 ), -1/( x-2 ) ) }}}
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check:
suppose {{{ x = 10 }}}
{{{ x + 2 = 12 }}}
{{{ z = -1/12 }}}
and
{{{ abs( x + 1/z ) = 2 }}}
{{{ abs( 10 + (-12) ) = 2 }}}
{{{ abs( -2 ) = 2 }}}
OK
{{{ x - 2 = 8 }}}
{{{ z = -1/8 }}}
and
{{{ abs( x + 1/z ) = 2
{{{ abs( 10 - 8 ) = 2 }}}
{{{ abs(2) = 2 }}}
OK