Question 189175
{{{9/((x+1))}}} - {{{2/((x-2))}}} = {{{5/((x+1))}}}
:
Multiply by (x+1)(x-2)*
(x+1)(x-2)*{{{9/((x+1))}}} - (x+1)(x-2)*{{{2/((x-2))}}} = (x+1)(x-2)*{{{5/((x+1))}}}
Cancel out the denominators and you have;
9(x-2) - 2(x+1) = 5(x-2)
:
9x - 18 - 2x - 2 = 5x - 10
:
x's on the left numerals on the right
9x - 2x - 5x = -10 + 2 + 18
:
2x = 10
x = {{{10/2}}}
x = 5
:
:
Check solution in original equation
{{{9/((x+5))}}} - {{{2/((5-2))}}} = {{{5/((5+1))}}}
{{{9/6}}} - {{{2/3}}} = {{{5/6}}}
{{{9/6}}} - {{{4/6}}} = {{{5/6}}}