Question 621492
Let n = "a number"
:
Assume the statement is:
"9 divided by the difference of a number and 1 minus 8 divided by a number plus 1, equals 9 times the reciprocal of the difference of the number squared and 1."
:
{{{9/((n-1))}}} - {{{8/((n+1))}}} = 9({{{1/((n^2-1))}}})
we can factor the 3rd denominator, as the "difference of squares"
{{{9/((n-1))}}} - {{{8/((n+1))}}} = 9({{{1/((n-1)(n+1))}}})
:
multiply by (x+1)(x-1), results gets rid of the denominators and we have
9(n+1) - 8(n-1) = 9
9n + 9 - 8n + 8 = 9
9n - 8n = 9 - 17
n = -8
:
:
Check this replace n with -8
{{{9/((-8-1))}}} - {{{8/((-8+1))}}} = 9({{{1/((-8^2-1))}}})
{{{9/(-9)}}} - {{{8/(-7)}}} = 9({{{1/((64-1))}}})
{{{-1}}} + {{{8/7}}} = {{{9/63}}}
-1 + {{{8/7}}} = {{{1/7}}}