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

Answer 1

#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#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

#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!

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To simplify the equation 5 / (y - 2) = y + 2, we can start by multiplying both sides of the equation by (y - 2) to eliminate the denominator. This gives us 5 = (y + 2)(y - 2). Expanding the right side of the equation, we get 5 = y^2 - 4. Rearranging the equation, we have y^2 - 4 - 5 = 0. Simplifying further, we have y^2 - 9 = 0. Factoring the equation, we get (y - 3)(y + 3) = 0. Therefore, the solutions to the equation are y = 3 and y = -3.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7