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 .
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
To solve the expression 5/sqrt(20) - 2 sqrt(45), let's break it down step by step:
Step 1: Simplify each square root expression.
- sqrt(20) = sqrt(4 * 5) = sqrt(4) * sqrt(5) = 2 sqrt(5)
- sqrt(45) = sqrt(9 * 5) = sqrt(9) * sqrt(5) = 3 sqrt(5)
Step 2: Substitute the simplified expressions back into the original equation.
- 5/sqrt(20) - 2 sqrt(45) = 5/(2 sqrt(5)) - 2 (3 sqrt(5))
Step 3: Rationalize the denominator (i.e., make sure there are no square roots in the denominator).
For the term 5/(2 sqrt(5)):
- Multiply the numerator and denominator by sqrt(5) to eliminate the square root in the denominator.
- (5 * sqrt(5)) / (2 sqrt(5) * sqrt(5)) = (5 sqrt(5)) / (2 * 5) = sqrt(5) / 2
For the term -2 (3 sqrt(5)):
- Multiply the whole term by sqrt(5) to remove the square root.
- -2 (3 sqrt(5)) = -6 sqrt(5)
Now we have:
sqrt(5) / 2 - 6 sqrt(5)
To simplify further, combine like terms:
(sqrt(5) - 12 sqrt(5)) / 2 = -11 sqrt(5) / 2
So the final answer is: -11 sqrt(5) / 2
Moving on to the next problem: 3/y+2 + 2/y = 5y - 4 / y^2 - 4
Step 1: Factor the denominator of y^2 - 4, which can be expressed as (y + 2)(y - 2).
Step 2: Find the least common denominator (LCD) of the fractions involved, which is y(y - 2)(y + 2).
Step 3: Multiply both sides of the equation by the LCD to eliminate the denominators.
The equation becomes:
3(y)(y - 2) + 2(y)(y + 2) = (5y - 4)(y)(y + 2)
Expanding the equation, we get:
3y^2 - 6y + 2y^2 + 4y = 5y^3 + 10y - 4y^2 - 8
Step 4: Combine like terms on both sides of the equation.
5y^2 - 2y = 5y^3 - 4y^2 + 10y - 8
Step 5: Move all terms to one side of the equation to set it equal to zero.
5y^3 - 9y^2 + 12y - 8 = 0
At this point, you may use various methods to solve for y, such as factoring, graphing, or using a numerical method like Newton's method.