# Solve for y 1/(y^2)=1/(2y^2)+(y-5)/(2y^2)

1y2=12y2+y-52y2
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
y2,2y2,2y2
Since y2,2y2,2y2 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,2,2 then find LCM for the variable part y2,y2,y2.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
Since 2 has no factors besides 1 and 2.
2 is a prime number
The LCM of 1,2,2 is the result of multiplying all prime factors the greatest number of times they occur in either number.
2
The factors for y2 are y⋅y, which is y multiplied by each other 2 times.
y2=y⋅y
y occurs 2 times.
The LCM of y2,y2,y2 is the result of multiplying all prime factors the greatest number of times they occur in either term.
y⋅y
Multiply y by y.
y2
The LCM for y2,2y2,2y2 is the numeric part 2 multiplied by the variable part.
2y2
2y2
Multiply each term by 2y2 and simplify.
Multiply each term in 1y2=12y2+y-52y2 by 2y2 in order to remove all the denominators from the equation.
1y2⋅(2y2)=12y2⋅(2y2)+y-52y2⋅(2y2)
Simplify 1y2⋅(2y2).
Rewrite using the commutative property of multiplication.
21y2y2=12y2⋅(2y2)+y-52y2⋅(2y2)
Combine 2 and 1y2.
2y2y2=12y2⋅(2y2)+y-52y2⋅(2y2)
Cancel the common factor of y2.
Cancel the common factor.
2y2y2=12y2⋅(2y2)+y-52y2⋅(2y2)
Rewrite the expression.
2=12y2⋅(2y2)+y-52y2⋅(2y2)
2=12y2⋅(2y2)+y-52y2⋅(2y2)
2=12y2⋅(2y2)+y-52y2⋅(2y2)
Simplify 12y2⋅(2y2)+y-52y2⋅(2y2).
Simplify each term.
Rewrite using the commutative property of multiplication.
2=212y2y2+y-52y2⋅(2y2)
Cancel the common factor of 2.
Factor 2 out of 2y2.
2=212(y2)y2+y-52y2⋅(2y2)
Cancel the common factor.
2=212y2y2+y-52y2⋅(2y2)
Rewrite the expression.
2=1y2y2+y-52y2⋅(2y2)
2=1y2y2+y-52y2⋅(2y2)
Cancel the common factor of y2.
Cancel the common factor.
2=1y2y2+y-52y2⋅(2y2)
Rewrite the expression.
2=1+y-52y2⋅(2y2)
2=1+y-52y2⋅(2y2)
Rewrite using the commutative property of multiplication.
2=1+2y-52y2y2
Cancel the common factor of 2.
Factor 2 out of 2y2.
2=1+2y-52(y2)y2
Cancel the common factor.
2=1+2y-52y2y2
Rewrite the expression.
2=1+y-5y2y2
2=1+y-5y2y2
Cancel the common factor of y2.
Cancel the common factor.
2=1+y-5y2y2
Rewrite the expression.
2=1+y-5
2=1+y-5
2=1+y-5
Subtract 5 from 1.
2=y-4
2=y-4
2=y-4
Solve the equation.
Rewrite the equation as y-4=2.
y-4=2
Move all terms not containing y to the right side of the equation.
Add 4 to both sides of the equation.
y=2+4