Basic Math Examples

Solve for u (u+2)/(3u-1)+1=(6-u)/(u+1)
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
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 1.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.4
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 1.5
The factor for is itself.
occurs time.
Step 1.6
The factor for is itself.
occurs time.
Step 1.7
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
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
Cancel the common factor of .
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Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Rewrite the expression.
Step 2.2.1.2
Expand using the FOIL Method.
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Step 2.2.1.2.1
Apply the distributive property.
Step 2.2.1.2.2
Apply the distributive property.
Step 2.2.1.2.3
Apply the distributive property.
Step 2.2.1.3
Simplify and combine like terms.
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Step 2.2.1.3.1
Simplify each term.
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Step 2.2.1.3.1.1
Multiply by .
Step 2.2.1.3.1.2
Multiply by .
Step 2.2.1.3.1.3
Multiply by .
Step 2.2.1.3.2
Add and .
Step 2.2.1.4
Multiply by .
Step 2.2.1.5
Expand using the FOIL Method.
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Step 2.2.1.5.1
Apply the distributive property.
Step 2.2.1.5.2
Apply the distributive property.
Step 2.2.1.5.3
Apply the distributive property.
Step 2.2.1.6
Simplify and combine like terms.
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Step 2.2.1.6.1
Simplify each term.
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Step 2.2.1.6.1.1
Multiply by by adding the exponents.
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Step 2.2.1.6.1.1.1
Move .
Step 2.2.1.6.1.1.2
Multiply by .
Step 2.2.1.6.1.2
Multiply by .
Step 2.2.1.6.1.3
Rewrite as .
Step 2.2.1.6.1.4
Multiply by .
Step 2.2.1.6.2
Subtract from .
Step 2.2.2
Simplify by adding terms.
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Step 2.2.2.1
Add and .
Step 2.2.2.2
Add and .
Step 2.2.2.3
Subtract from .
Step 2.3
Simplify the right side.
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Step 2.3.1
Cancel the common factor of .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factor.
Step 2.3.1.3
Rewrite the expression.
Step 2.3.2
Expand using the FOIL Method.
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Step 2.3.2.1
Apply the distributive property.
Step 2.3.2.2
Apply the distributive property.
Step 2.3.2.3
Apply the distributive property.
Step 2.3.3
Simplify and combine like terms.
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Step 2.3.3.1
Simplify each term.
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Step 2.3.3.1.1
Multiply by .
Step 2.3.3.1.2
Multiply by .
Step 2.3.3.1.3
Rewrite using the commutative property of multiplication.
Step 2.3.3.1.4
Multiply by by adding the exponents.
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Step 2.3.3.1.4.1
Move .
Step 2.3.3.1.4.2
Multiply by .
Step 2.3.3.1.5
Multiply by .
Step 2.3.3.1.6
Multiply .
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Step 2.3.3.1.6.1
Multiply by .
Step 2.3.3.1.6.2
Multiply by .
Step 2.3.3.2
Add and .
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
Add to both sides of the equation.
Step 3.1.3
Add and .
Step 3.1.4
Subtract from .
Step 3.2
Add to both sides of the equation.
Step 3.3
Add and .
Step 3.4
Factor the left side of the equation.
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Step 3.4.1
Factor out of .
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Step 3.4.1.1
Factor out of .
Step 3.4.1.2
Factor out of .
Step 3.4.1.3
Factor out of .
Step 3.4.1.4
Factor out of .
Step 3.4.1.5
Factor out of .
Step 3.4.2
Factor using the perfect square rule.
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Step 3.4.2.1
Rewrite as .
Step 3.4.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 3.4.2.3
Rewrite the polynomial.
Step 3.4.2.4
Factor using the perfect square trinomial rule , where and .
Step 3.5
Divide each term in by and simplify.
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Step 3.5.1
Divide each term in by .
Step 3.5.2
Simplify the left side.
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Step 3.5.2.1
Cancel the common factor of .
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Step 3.5.2.1.1
Cancel the common factor.
Step 3.5.2.1.2
Divide by .
Step 3.5.3
Simplify the right side.
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Step 3.5.3.1
Divide by .
Step 3.6
Set the equal to .
Step 3.7
Add to both sides of the equation.