Question 225144
-_7___          _3__
 y + 1  =  -4 -  y-4
Assume it's
{{{-7/(y+1)}}} = -4 - {{{3/(y-4)}}}
Multiply by (y+1)(y-4)*
(y+1)(y-4)*{{{-7/(y+1)}}} = -4(y+1)(y-4) - (y+1)(y-4)*{{{3/(y-4)}}}
:
cancel the denominators and you have
-7(y-4) = -4(y+1)(y-4) - 3(y+1)
:
-7y + 28 = -4(y^2 - 4y + y - 4) - 3y - 3
:
-7y + 28 = -4(y^2 - 3y - 4) - 3y - 3
:
-7y + 28 = -4y^2 + 12y + 16 - 3y - 3
:
-7y + 28 = -4y^2 + 9y + 13
:
4y^2 - 7y - 9y + 28 - 13 = 0
:
4y^2 - 16y + 15 = 0
Factor this to
(2x - 5)(2x - 3) = 0
Two solutions
2x = 5
x = 2.5
and
2x = 3
x = 1.5
:
x = 2.5, 1.5
:
:
Check solution using x=2.5
{{{-7/(2.5+1)}}} = -4 - {{{3/(2.5-4)}}}
{{{-7/(3.5)}}} = -4 - {{{3/(-1.5)}}}
-2 = -4 + 2
:
you can check it using the x=1.5 solution