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

Answer 1

Isaiah Anthony

#y=pm3#

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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Answer 2

Julia Adams

#y=+-3#

#"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#

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Answer 3

Isaiah Anthony

To solve the rational equation 5/(y-2) = y+2, you can start by multiplying both sides of the equation by (y-2) to eliminate the denominator. This gives you 5 = (y+2)(y-2). Expanding the right side of the equation, you get 5 = y^2 - 4. Rearranging the equation, you have y^2 - 4 - 5 = 0. Simplifying further, you get y^2 - 9 = 0. Factoring the equation, you have (y-3)(y+3) = 0. Setting each factor equal to zero, you get y-3 = 0 or y+3 = 0. Solving for y, you find y = 3 or y = -3. Therefore, the solutions to the rational equation are y = 3 and y = -3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.