fractional Equations?

Question

omg i need help again on y+2/y-3 - y-3/y+2 =5/6 please help

Answer 1

Hi,

Answers are y = 0 and y = 13.

y.+.2....y.-.3......5
------ - ------- = ---
y.-.3.....y.+.2.....6

Multiply the first fraction by y + 2 on top and bottom. Multiply the second fraction by y - 3 on top and bottom.

(y.+.2)^2....(y.-.3)^2......5
------------- - ----------- = ---
(y-3)(y+2)..(y+2)(y-3)...6


..10y - 5........5
------------- = ---
(y-3)(y+2)....6

Cross multiply and simplify.

5(y-3)(y+2) = 6(10y - 5)
5y^2 - 5y -30 = 60y - 30
5y^2 - 65y = 0
5y(y - 13) = 0
y = 0 or y = 13

Both answers check.

I hope that helps. :-)

Answer 2

(y + 2)/(y - 3) - (y - 3)/(y + 2) = 5 / 6
6.(y + 2)² - 6.(y - 3)² = 5.(y - 3).(y + 2)
LHS = 6(y² + 4y + 4) - 6.(y² - 6y + 9)
LHS = 60y - 30

RHS = 5.(y - 3).(y + 2)
RHS = 5.(y² - y - 6)
RHS = 5y² - 5y - 30

Which leads to:-
60y - 30 = 5y² - 5y - 30
5y² - 65y = 0
5y.(y - 13) = 0
y = 0, y = 13