How do you solve #5/y - 2 = y + 2#?

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Answer 1 · 2015-06-04T09:10:34

#5/y - 2 = y + 2#

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

cross multiplying:
#5 - 2y= y(y + 2)#

#5 - 2y= y^2 +2y#

# color(blue)(y^2 +4y - 5 = 0#

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

# y^2 +4y - 5 =y^2 +5y - y- 5 #

#y(y+5) -1( y+ 5)= 0#

#color(blue)((y-1)(y+5) = 0#

the solutions for the expression are: #color(blue)(y = 1 , y = -5#