Finite Math Examples

Solve for x (2x)/(x-1)+1/4=7/8+2/(x-1)
Step 1
Find the LCD of the terms in the equation.
Tap for more steps...
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
has factors of and .
Step 1.5
The prime factors for are .
Tap for more steps...
Step 1.5.1
has factors of and .
Step 1.5.2
has factors of and .
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
Multiply .
Tap for more steps...
Step 1.8.1
Multiply by .
Step 1.8.2
Multiply by .
Step 1.9
The factor for is itself.
occurs time.
Step 1.10
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 1.11
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Step 2
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Tap for more steps...
Step 2.2.1
Simplify each term.
Tap for more steps...
Step 2.2.1.1
Rewrite using the commutative property of multiplication.
Step 2.2.1.2
Multiply .
Tap for more steps...
Step 2.2.1.2.1
Combine and .
Step 2.2.1.2.2
Multiply by .
Step 2.2.1.3
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.3.1
Cancel the common factor.
Step 2.2.1.3.2
Rewrite the expression.
Step 2.2.1.4
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.4.1
Factor out of .
Step 2.2.1.4.2
Cancel the common factor.
Step 2.2.1.4.3
Rewrite the expression.
Step 2.2.1.5
Apply the distributive property.
Step 2.2.1.6
Multiply by .
Step 2.2.2
Add and .
Step 2.3
Simplify the right side.
Tap for more steps...
Step 2.3.1
Simplify each term.
Tap for more steps...
Step 2.3.1.1
Cancel the common factor of .
Tap for more steps...
Step 2.3.1.1.1
Cancel the common factor.
Step 2.3.1.1.2
Rewrite the expression.
Step 2.3.1.2
Apply the distributive property.
Step 2.3.1.3
Multiply by .
Step 2.3.1.4
Rewrite using the commutative property of multiplication.
Step 2.3.1.5
Multiply .
Tap for more steps...
Step 2.3.1.5.1
Combine and .
Step 2.3.1.5.2
Multiply by .
Step 2.3.1.6
Cancel the common factor of .
Tap for more steps...
Step 2.3.1.6.1
Cancel the common factor.
Step 2.3.1.6.2
Rewrite the expression.
Step 2.3.2
Add and .
Step 3
Solve the equation.
Tap for more steps...
Step 3.1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 3.2.1
Add to both sides of the equation.
Step 3.2.2
Add and .
Step 3.3
Divide each term in by and simplify.
Tap for more steps...
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Tap for more steps...
Step 3.3.3.1
Divide by .
Step 4
Exclude the solutions that do not make true.