Basic Math Examples

Solve for a 18/(6a-18)-6/(6-6a)=1/(a^2-4a+3)
Step 1
Factor each term.
Tap for more steps...
Step 1.1
Factor out of .
Tap for more steps...
Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.2
Reduce the expression by cancelling the common factors.
Tap for more steps...
Step 1.2.1
Factor out of .
Step 1.2.2
Cancel the common factor.
Step 1.2.3
Rewrite the expression.
Step 1.3
Factor out of .
Tap for more steps...
Step 1.3.1
Factor out of .
Step 1.3.2
Factor out of .
Step 1.3.3
Factor out of .
Step 1.4
Reduce the expression by cancelling the common factors.
Tap for more steps...
Step 1.4.1
Cancel the common factor.
Step 1.4.2
Rewrite the expression.
Step 1.5
Factor using the AC method.
Tap for more steps...
Step 1.5.1
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 1.5.2
Write the factored form using these integers.
Step 2
Find the LCD of the terms in the equation.
Tap for more steps...
Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
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 2.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.4
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.5
The factor for is itself.
occurs time.
Step 2.6
The factor for is itself.
occurs time.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The factor for is itself.
occurs time.
Step 2.9
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Simplify each term.
Tap for more steps...
Step 3.2.1.1
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.1.1
Factor out of .
Step 3.2.1.1.2
Cancel the common factor.
Step 3.2.1.1.3
Rewrite the expression.
Step 3.2.1.2
Rewrite as .
Step 3.2.1.3
Factor out of .
Step 3.2.1.4
Factor out of .
Step 3.2.1.5
Reorder terms.
Step 3.2.1.6
Raise to the power of .
Step 3.2.1.7
Raise to the power of .
Step 3.2.1.8
Use the power rule to combine exponents.
Step 3.2.1.9
Add and .
Step 3.2.1.10
Multiply by .
Step 3.2.1.11
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.11.1
Move the leading negative in into the numerator.
Step 3.2.1.11.2
Factor out of .
Step 3.2.1.11.3
Cancel the common factor.
Step 3.2.1.11.4
Rewrite the expression.
Step 3.2.1.12
Expand using the FOIL Method.
Tap for more steps...
Step 3.2.1.12.1
Apply the distributive property.
Step 3.2.1.12.2
Apply the distributive property.
Step 3.2.1.12.3
Apply the distributive property.
Step 3.2.1.13
Simplify and combine like terms.
Tap for more steps...
Step 3.2.1.13.1
Simplify each term.
Tap for more steps...
Step 3.2.1.13.1.1
Multiply by .
Step 3.2.1.13.1.2
Move to the left of .
Step 3.2.1.13.1.3
Rewrite as .
Step 3.2.1.13.1.4
Multiply by .
Step 3.2.1.13.2
Subtract from .
Step 3.2.1.14
Apply the distributive property.
Step 3.2.1.15
Simplify.
Tap for more steps...
Step 3.2.1.15.1
Multiply by .
Step 3.2.1.15.2
Multiply by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.1
Factor out of .
Step 3.3.1.2
Cancel the common factor.
Step 3.3.1.3
Rewrite the expression.
Step 4
Solve the equation.
Tap for more steps...
Step 4.1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 4.1.1
Add to both sides of the equation.
Step 4.1.2
Simplify each term.
Tap for more steps...
Step 4.1.2.1
Rewrite as .
Step 4.1.2.2
Expand using the FOIL Method.
Tap for more steps...
Step 4.1.2.2.1
Apply the distributive property.
Step 4.1.2.2.2
Apply the distributive property.
Step 4.1.2.2.3
Apply the distributive property.
Step 4.1.2.3
Simplify and combine like terms.
Tap for more steps...
Step 4.1.2.3.1
Simplify each term.
Tap for more steps...
Step 4.1.2.3.1.1
Multiply by .
Step 4.1.2.3.1.2
Move to the left of .
Step 4.1.2.3.1.3
Rewrite as .
Step 4.1.2.3.1.4
Rewrite as .
Step 4.1.2.3.1.5
Multiply by .
Step 4.1.2.3.2
Subtract from .
Step 4.1.2.4
Apply the distributive property.
Step 4.1.2.5
Simplify.
Tap for more steps...
Step 4.1.2.5.1
Multiply by .
Step 4.1.2.5.2
Multiply by .
Step 4.1.3
Subtract from .
Step 4.1.4
Add and .
Step 4.1.5
Add and .
Step 4.1.6
Subtract from .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Subtract from .
Step 4.4
Factor the left side of the equation.
Tap for more steps...
Step 4.4.1
Factor out of .
Tap for more steps...
Step 4.4.1.1
Factor out of .
Step 4.4.1.2
Factor out of .
Step 4.4.1.3
Rewrite as .
Step 4.4.1.4
Factor out of .
Step 4.4.1.5
Factor out of .
Step 4.4.2
Factor.
Tap for more steps...
Step 4.4.2.1
Factor by grouping.
Tap for more steps...
Step 4.4.2.1.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps...
Step 4.4.2.1.1.1
Factor out of .
Step 4.4.2.1.1.2
Rewrite as plus
Step 4.4.2.1.1.3
Apply the distributive property.
Step 4.4.2.1.2
Factor out the greatest common factor from each group.
Tap for more steps...
Step 4.4.2.1.2.1
Group the first two terms and the last two terms.
Step 4.4.2.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 4.4.2.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 4.4.2.2
Remove unnecessary parentheses.
Step 4.5
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.6
Set equal to and solve for .
Tap for more steps...
Step 4.6.1
Set equal to .
Step 4.6.2
Add to both sides of the equation.
Step 4.7
Set equal to and solve for .
Tap for more steps...
Step 4.7.1
Set equal to .
Step 4.7.2
Solve for .
Tap for more steps...
Step 4.7.2.1
Add to both sides of the equation.
Step 4.7.2.2
Divide each term in by and simplify.
Tap for more steps...
Step 4.7.2.2.1
Divide each term in by .
Step 4.7.2.2.2
Simplify the left side.
Tap for more steps...
Step 4.7.2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 4.7.2.2.2.1.1
Cancel the common factor.
Step 4.7.2.2.2.1.2
Divide by .
Step 4.8
The final solution is all the values that make true.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: