Basic Math Examples

Simplify (y+1)/y+(y-1)/5=2
Step 1
Find the LCD of the terms in the equation.
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Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 1.3
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.
Step 1.4
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.5
Since has no factors besides and .
is a prime number
Step 1.6
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.7
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 1.8
The factor for is itself.
occurs time.
Step 1.9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 1.10
The LCM for is the numeric part multiplied by the variable part.
Step 2
Multiply each term in by to eliminate the fractions.
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Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Rewrite using the commutative property of multiplication.
Step 2.2.1.2
Combine and .
Step 2.2.1.3
Cancel the common factor of .
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Step 2.2.1.3.1
Cancel the common factor.
Step 2.2.1.3.2
Rewrite the expression.
Step 2.2.1.4
Apply the distributive property.
Step 2.2.1.5
Multiply by .
Step 2.2.1.6
Rewrite using the commutative property of multiplication.
Step 2.2.1.7
Cancel the common factor of .
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Step 2.2.1.7.1
Cancel the common factor.
Step 2.2.1.7.2
Rewrite the expression.
Step 2.2.1.8
Apply the distributive property.
Step 2.2.1.9
Multiply by .
Step 2.2.1.10
Rewrite as .
Step 2.2.2
Subtract from .
Step 2.3
Simplify the right side.
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Step 2.3.1
Multiply by .
Step 3
Solve the equation.
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Step 3.1
Move all terms containing to the left side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Factor using the AC method.
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Step 3.2.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2.2
Write the factored form using these integers.
Step 3.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.4
Set equal to and solve for .
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Step 3.4.1
Set equal to .
Step 3.4.2
Add to both sides of the equation.
Step 3.5
Set equal to and solve for .
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Step 3.5.1
Set equal to .
Step 3.5.2
Add to both sides of the equation.
Step 3.6
The final solution is all the values that make true.