Question 594748
{{{5/(y+5)-9/(y-5)=10/(y^2-25)}}}
The third denominator is the "difference of squares" factors to:
{{{5/(y+5)-9/(y-5)=10/((y+5)(y-5))}}}
Multiply by (y+5)(y-5) to clear the denominators, results
5(y-5) -9(y+5) = 10
:
5y - 25 - 9y - 45 = 10
-4y - 70 = 10
-4y = 10 + 70
-4y = 80
y = 80/-4
y = -20
:
:
Check solution in original equation
{{{5/(-20+5)-9/(-20-5)=10/(-20^2-25)}}}
{{{(-5/15) - (-9/25) = 10/(400 - 25)}}}