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

2 Answers
Mar 7, 2018

Answer:

#color(magenta)(therefore y=3 or y=-3#

Explanation:

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

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

Identity:
#color(red)((a+b)(a-b)=a^2-b^2#

#y^2-4=5#

#y^2-4-5=0#

#y^2-9=0#

Identity:
#color(red)((a+b)(a-b)=a^2-b^2#

#(y+3)(y-3)=0#

#therefore y-3=0 or y+3=0#

#color(magenta)(therefore y=3 or y=-3#

Mar 7, 2018

Answer:

#y=+-3#

Explanation:

#"multiply both sides by "(y-2)#

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

#rArr(y-2)(y+2)=5larrcolor(blue)"expand factors"#

#rArry^2-4=5larrcolor(blue)"add 4 to both sides"#

#rArry^2=9#

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

#rArry=+-3larrcolor(blue)"note plus or minus"#

#color(blue)"As a check"#

#y=3to5/(3-2)=3+2to5=5" True"#

#y=-3to5/(-3-2)=-3+2to-1=-1" True"#

#rArry=+-3" are the solutions"#