Please help:
(y^2+4y/y^2+2y-8)/(y/y+2)
I think I have the correct answer.. just want to make sure.. the answer is
y+2/y-2 right?
if you mean:
(y+2)/(y-2)
then you're correct
To simplify the expression, let's break it down step by step.
Step 1: Simplify the numerator (y^2+4y)/(y^2+2y-8):
Factor both the numerator and denominator if possible:
y^2 + 4y = y(y + 4)
y^2 + 2y - 8 = (y + 4)(y - 2)
Now the expression becomes:
(y(y + 4)/(y + 4)(y - 2)) / (y/(y + 2))
Step 2: Simplify the denominator y/(y + 2):
The denominator is already in its simplest form.
Step 3: Simplify the numerator (y(y + 4))/(y + 4)(y - 2):
The denominator (y + 4)(y - 2) cancels out with the common factor in the numerator (y + 4).
The expression becomes:
y/(y - 2) / (y/(y + 2))
Step 4: Simplify the expression:
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
(y/(y - 2)) * ((y + 2)/y)
Simplify the expression:
(y * (y + 2)) / ((y - 2) * y)
Now, let's simplify further:
(y^2 + 2y) / (y^2 - 2y)
Therefore, the simplified expression is (y^2 + 2y) / (y^2 - 2y).