How do you solve the rational equation #(y+2)/y = 1 / (y-5)#?

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Answer 1 · 2016-07-10T05:23:32

# y= 2+-sqrt14#

Taking, #sqrt14~=3.742#,

#y=5.742, or, -1.742#

#(y+2)/y=1/(y-5).#

#:. (y+2)(y-5)=y.#

#:. y^2+(-5+2)y-10-y=0.#

#:. y^2-3y-y=10.#

#:. y^2-4y=10#.

#:.y^2-4y+4=10+4#............[completing square]

#:. (y-2)^2=(sqrt14)^2#

#:. y-2=+-sqrt14#

#:. y= 2+-sqrt14#

Taking, #sqrt14~=3.742#,

#y=5.742, or, -1.742#

Enjoy Maths.!