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

2 Answers
Jim G.
Jul 17, 2018

#y=+-3#

Explanation:

#"multiply both sides by "y-2#

#cancel(y-2)xx5/cancel(y-2)=(y+2)(y-2)#

#5=y^2-4#

#"add 4 to both sides"#

#9=y^2#

#color(blue)"take the square root of both sides"#

#+-sqrt9=ylarrcolor(blue)"note plus or minus"#

#rArry=+-3#

Sonnhard
Jul 17, 2018

#y=pm3#

Explanation:

First of all it must be #yne 2#, and we can multiply the whole equation by #y-2# and we get

#5=(y-2)(y+2)# now we use that

#(a-b)(a+b)=a^2-b^2#

so we get

#5=y^2-4#

adding #4#

#9=y^2#

so we get #y=pm 3#

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