Solve for y y/(8y-64)-8=1/(y-8)

Math
y8y-64-8=1y-8
Factor 8 out of 8y-64.
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Factor 8 out of 8y.
y8(y)-64-8=1y-8
Factor 8 out of -64.
y8y+8⋅-8-8=1y-8
Factor 8 out of 8y+8⋅-8.
y8(y-8)-8=1y-8
y8(y-8)-8=1y-8
Find the LCD of the terms in the equation.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
8(y-8),1,y-8
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 prime factors for 8 are 2⋅2⋅2.
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8 has factors of 2 and 4.
2⋅4
4 has factors of 2 and 2.
2⋅2⋅2
2⋅2⋅2
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 8,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
2⋅2⋅2
The LCM of 8,1,1 is 2⋅2⋅2=8.
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Multiply 2 by 2.
4⋅2
Multiply 4 by 2.
8
8
The factor for y-8 is y-8 itself.
(y-8)=y-8
(y-8) occurs 1 time.
The LCM of y-8,y-8 is the result of multiplying all factors the greatest number of times they occur in either term.
y-8
The Least Common Multiple LCM of some numbers is the smallest number that the numbers are factors of.
8(y-8)
8(y-8)
Multiply each term by 8(y-8) and simplify.
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Multiply each term in y8(y-8)-8=1y-8 by 8(y-8) in order to remove all the denominators from the equation.
y8(y-8)⋅(8(y-8))-8⋅(8(y-8))=1y-8⋅(8(y-8))
Simplify y8(y-8)⋅(8(y-8))-8⋅(8(y-8)).
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Simplify each term.
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Rewrite using the commutative property of multiplication.
8y8(y-8)(y-8)-8⋅(8(y-8))=1y-8⋅(8(y-8))
Cancel the common factor of 8.
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Cancel the common factor.
8y8(y-8)(y-8)-8⋅(8(y-8))=1y-8⋅(8(y-8))
Rewrite the expression.
yy-8(y-8)-8⋅(8(y-8))=1y-8⋅(8(y-8))
yy-8(y-8)-8⋅(8(y-8))=1y-8⋅(8(y-8))
Cancel the common factor of y-8.
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Cancel the common factor.
yy-8(y-8)-8⋅(8(y-8))=1y-8⋅(8(y-8))
Rewrite the expression.
y-8⋅(8(y-8))=1y-8⋅(8(y-8))
y-8⋅(8(y-8))=1y-8⋅(8(y-8))
Apply the distributive property.
y-8⋅(8y+8⋅-8)=1y-8⋅(8(y-8))
Multiply 8 by -8.
y-8⋅(8y-64)=1y-8⋅(8(y-8))
Apply the distributive property.
y-8(8y)-8⋅-64=1y-8⋅(8(y-8))
Multiply 8 by -8.
y-64y-8⋅-64=1y-8⋅(8(y-8))
Multiply -8 by -64.
y-64y+512=1y-8⋅(8(y-8))
y-64y+512=1y-8⋅(8(y-8))
Subtract 64y from y.
-63y+512=1y-8⋅(8(y-8))
-63y+512=1y-8⋅(8(y-8))
Simplify 1y-8⋅(8(y-8)).
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Rewrite using the commutative property of multiplication.
-63y+512=81y-8(y-8)
Combine 8 and 1y-8.
-63y+512=8y-8(y-8)
Cancel the common factor of y-8.
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Cancel the common factor.
-63y+512=8y-8(y-8)
Rewrite the expression.
-63y+512=8
-63y+512=8
-63y+512=8
-63y+512=8
Solve the equation.
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Move all terms not containing y to the right side of the equation.
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Subtract 512 from both sides of the equation.
-63y=8-512
Subtract 512 from 8.
-63y=-504
-63y=-504
Divide each term by -63 and simplify.
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Divide each term in -63y=-504 by -63.
-63y-63=-504-63
Cancel the common factor of -63.
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Cancel the common factor.
-63y-63=-504-63
Divide y by 1.
y=-504-63
y=-504-63
Divide -504 by -63.
y=8
y=8
y=8
Exclude the solutions that do not make y8y-64-8=1y-8 true.
No solution
Solve for y y/(8y-64)-8=1/(y-8)

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