Finite Math Examples

Solve for x x-(3x)/(x-3)=9-9/(x-3)
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
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 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.
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
Apply the distributive property.
Step 2.2.1.2
Multiply by .
Step 2.2.1.3
Move to the left of .
Step 2.2.1.4
Cancel the common factor of .
Tap for more steps...
Step 2.2.1.4.1
Move the leading negative in into the numerator.
Step 2.2.1.4.2
Cancel the common factor.
Step 2.2.1.4.3
Rewrite the expression.
Step 2.2.2
Subtract from .
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
Apply the distributive property.
Step 2.3.1.2
Multiply by .
Step 2.3.1.3
Cancel the common factor of .
Tap for more steps...
Step 2.3.1.3.1
Move the leading negative in into the numerator.
Step 2.3.1.3.2
Cancel the common factor.
Step 2.3.1.3.3
Rewrite the expression.
Step 2.3.2
Subtract from .
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
Add to both sides of the equation.
Step 3.3
Factor using the AC method.
Tap for more steps...
Step 3.3.1
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 3.3.2
Write the factored form using these integers.
Step 3.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.5
Set equal to and solve for .
Tap for more steps...
Step 3.5.1
Set equal to .
Step 3.5.2
Add to both sides of the equation.
Step 3.6
Set equal to and solve for .
Tap for more steps...
Step 3.6.1
Set equal to .
Step 3.6.2
Add to both sides of the equation.
Step 3.7
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.