5/square root 20 - 2 square root 45

Help please I have no clue how to do this ok studying for a test

3/y+2 + 2/y = 5y-4/y^2-4

I know you factor then multiply by LCD y(y-2)(y+2)

I get stuck right after that step and don't know what to do .

2 answers

Square root 20 and Square root 45 can be simplified even further.

Square root 20 is simply Square root 4 times Square root 5. Square root 4 is equal to 2. Therefore, Square root 20 is equal to 2 Square root 5.

Square root 45 can also be simplified into Square root 9 times Square root 5. Square root 9 is equivalent to 3. Thus you multiply 3 with 2 on the outside and leave Square root 5 alone to get 6 Square root 5.

Thus far we get, 5/ 2 Square root 5 and we know this is not possible because the denominator cannot a square root. To solve this, simply multiply the numerator and denominator by 2 Square root 5. By doing so, the denominator cancels out and the numerator will result in 5 times 2 Square root 5 which is 10 Square root 5.

From earlier we got 6 Square root 5 as a result of the simplification.

Simply do 10 Square root 5 - 6 Square root 5 which will get you 4 Square root 5.
5/√20 - 2√45
= 5/(2√5) - 6√5
= 5/(2√5) *√5/√5 - 6√5
= 5√5/10 - 6√5
= √5/2 - 12√5/2
= -(11√5)/2

I have a strong feeling you meant

3/(y+2) + 2/y = (5y-4)/(y^2-4)
do you know why we would multiply by y(x+2)(y-2) ??

we would get:
3y(y-2) + 2(y+2)(y-2) = y(5y-4)
3y^2 - 6y + 2y^2 - 8 = 5y^2 - 4y
-2y = 8
y = -4
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