How do you solve #\frac { 15} { y - 5} - \frac { 3} { y } = \frac { 17y + 5} { y ^ { 2} - 25}#?

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Answer 1 · 2018-06-04T11:41:42

Solution: #y= -1, y=15#

# 15/(y-5) -3/y = (17 y +5)/((y^2-25)# or

# 15/(y-5) -3/y = (17 y +5)/((y-5)(y+5)# Multiplying

by #y(y-5)(y+5)# on both sides we get,

# 15 y(y+5) -3(y^2-25) = y (17 y +5)# or

# 15 y^2+ 75 y -3 y^2+75 - 17 y^2 -5 y=0# or

# -5 y^2+ 70 y +75 =0# or

# 5 y^2 - 70 y -75 =0# or

# y^2 - 14 y -15 =0 # or

# y^2 - 15 y +y -15 =0 # or

# y(y - 15) +1(y -15)=0 # or

#(y - 15)(y +1)=0 :. y =15 , y =1#

Solution: #y=-1, y=15# [Ans]