How do you simplify #5 / (y - 2)= y + 2 #?

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Answer 1 · 2018-04-27T03:38:34

#y=+-3#

By transposing the terms and using simple algebra, we get-

5=(y+2)(y-2)
Using #a^2-b^2=(a+b)(a-b)#,
5= #y^2-4#
#y^2=9#
#y=+-3#

Answer 2 · 2018-04-27T04:36:58

#y = +-3#

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

Multiply both sides by #y-2#:
#5/cancel((y-2)) cancel(color(red)(*(y-2))) = (y+2)color(red)((y-2))#

Simplify:
#5 = y^2 - 4#

Add #4# on both sides of the equation:

#5 quadcolor(red)(+quad4) = y^2 - 4 quadcolor(red)(+quad4)#

#9 = y^2#

Therefore, #y = +-3#

(#+-# refers to "plus or minus")

Hope this helps!