# Solve for y 7/(y-1)+1/y=9/8

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.
Since contain both numbers and variables, there are four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.
Steps to find the LCM for are:
1. Find the LCM for the numeric part .
2. Find the LCM for the variable part .
3. Find the LCM for the compound variable part .
4. Multiply each LCM together.
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 is not a prime number because it only has one positive factor, which is itself.
Not prime
The prime factors for are .
has factors of and .
has factors of and .
The LCM of is .
Multiply by .
Multiply by .
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify .
Simplify each term.
Rewrite using the commutative property of multiplication.
Multiply .
Combine and .
Multiply by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite using the commutative property of multiplication.
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply by .
Simplify .
Simplify terms.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Simplify the expression.
Multiply by .
Move to the left of .
Rewrite as .
Simplify by multiplying through.
Apply the distributive property.
Multiply by .
Solve the equation.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Move to the left side of the equation by adding it to both sides.
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Set the next factor equal to and solve.
Set the next factor equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for y 7/(y-1)+1/y=9/8

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