Enter a problem...
Finite Math Examples
, ,
Step 1
Step 1.1
Move all terms not containing to the right side of the equation.
Step 1.1.1
Add to both sides of the equation.
Step 1.1.2
Add to both sides of the equation.
Step 1.2
Divide each term in by and simplify.
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Step 1.2.2.1
Cancel the common factor of .
Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
Step 1.2.3.1
Simplify each term.
Step 1.2.3.1.1
Cancel the common factor of and .
Step 1.2.3.1.1.1
Factor out of .
Step 1.2.3.1.1.2
Cancel the common factors.
Step 1.2.3.1.1.2.1
Factor out of .
Step 1.2.3.1.1.2.2
Cancel the common factor.
Step 1.2.3.1.1.2.3
Rewrite the expression.
Step 1.2.3.1.2
Cancel the common factor of and .
Step 1.2.3.1.2.1
Factor out of .
Step 1.2.3.1.2.2
Cancel the common factors.
Step 1.2.3.1.2.2.1
Factor out of .
Step 1.2.3.1.2.2.2
Cancel the common factor.
Step 1.2.3.1.2.2.3
Rewrite the expression.
Step 1.2.3.1.3
Cancel the common factor of and .
Step 1.2.3.1.3.1
Factor out of .
Step 1.2.3.1.3.2
Cancel the common factors.
Step 1.2.3.1.3.2.1
Factor out of .
Step 1.2.3.1.3.2.2
Cancel the common factor.
Step 1.2.3.1.3.2.3
Rewrite the expression.
Step 2
Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify .
Step 2.2.1.1
Simplify each term.
Step 2.2.1.1.1
Apply the distributive property.
Step 2.2.1.1.2
Simplify.
Step 2.2.1.1.2.1
Cancel the common factor of .
Step 2.2.1.1.2.1.1
Factor out of .
Step 2.2.1.1.2.1.2
Factor out of .
Step 2.2.1.1.2.1.3
Cancel the common factor.
Step 2.2.1.1.2.1.4
Rewrite the expression.
Step 2.2.1.1.2.2
Combine and .
Step 2.2.1.1.2.3
Multiply by .
Step 2.2.1.1.2.4
Cancel the common factor of .
Step 2.2.1.1.2.4.1
Factor out of .
Step 2.2.1.1.2.4.2
Cancel the common factor.
Step 2.2.1.1.2.4.3
Rewrite the expression.
Step 2.2.1.1.2.5
Multiply by .
Step 2.2.1.1.2.6
Cancel the common factor of .
Step 2.2.1.1.2.6.1
Factor out of .
Step 2.2.1.1.2.6.2
Cancel the common factor.
Step 2.2.1.1.2.6.3
Rewrite the expression.
Step 2.2.1.1.2.7
Multiply by .
Step 2.2.1.1.3
Move the negative in front of the fraction.
Step 2.2.1.2
Simplify by adding terms.
Step 2.2.1.2.1
Add and .
Step 2.2.1.2.2
Subtract from .
Step 2.3
Replace all occurrences of in with .
Step 2.4
Simplify the left side.
Step 2.4.1
Simplify .
Step 2.4.1.1
Simplify each term.
Step 2.4.1.1.1
Apply the distributive property.
Step 2.4.1.1.2
Simplify.
Step 2.4.1.1.2.1
Cancel the common factor of .
Step 2.4.1.1.2.1.1
Factor out of .
Step 2.4.1.1.2.1.2
Factor out of .
Step 2.4.1.1.2.1.3
Cancel the common factor.
Step 2.4.1.1.2.1.4
Rewrite the expression.
Step 2.4.1.1.2.2
Combine and .
Step 2.4.1.1.2.3
Multiply by .
Step 2.4.1.1.2.4
Cancel the common factor of .
Step 2.4.1.1.2.4.1
Factor out of .
Step 2.4.1.1.2.4.2
Cancel the common factor.
Step 2.4.1.1.2.4.3
Rewrite the expression.
Step 2.4.1.1.2.5
Multiply by .
Step 2.4.1.1.2.6
Cancel the common factor of .
Step 2.4.1.1.2.6.1
Factor out of .
Step 2.4.1.1.2.6.2
Cancel the common factor.
Step 2.4.1.1.2.6.3
Rewrite the expression.
Step 2.4.1.1.2.7
Multiply by .
Step 2.4.1.1.3
Move the negative in front of the fraction.
Step 2.4.1.2
Simplify by adding terms.
Step 2.4.1.2.1
Subtract from .
Step 2.4.1.2.2
Add and .
Step 3
Step 3.1
Move all terms not containing to the right side of the equation.
Step 3.1.1
Add to both sides of the equation.
Step 3.1.2
Subtract from both sides of the equation.
Step 3.2
Divide each term in by and simplify.
Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Cancel the common factor of .
Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
Step 3.2.3.1
Simplify each term.
Step 3.2.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 3.2.3.1.2
Cancel the common factor of .
Step 3.2.3.1.2.1
Factor out of .
Step 3.2.3.1.2.2
Factor out of .
Step 3.2.3.1.2.3
Cancel the common factor.
Step 3.2.3.1.2.4
Rewrite the expression.
Step 3.2.3.1.3
Multiply by .
Step 3.2.3.1.4
Multiply by .
Step 3.2.3.1.5
Move the negative in front of the fraction.
Step 3.2.3.1.6
Cancel the common factor of and .
Step 3.2.3.1.6.1
Factor out of .
Step 3.2.3.1.6.2
Cancel the common factors.
Step 3.2.3.1.6.2.1
Factor out of .
Step 3.2.3.1.6.2.2
Cancel the common factor.
Step 3.2.3.1.6.2.3
Rewrite the expression.
Step 4
Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the left side.
Step 4.2.1
Simplify .
Step 4.2.1.1
Simplify each term.
Step 4.2.1.1.1
Apply the distributive property.
Step 4.2.1.1.2
Multiply .
Step 4.2.1.1.2.1
Multiply by .
Step 4.2.1.1.2.2
Combine and .
Step 4.2.1.1.2.3
Multiply by .
Step 4.2.1.1.3
Multiply .
Step 4.2.1.1.3.1
Combine and .
Step 4.2.1.1.3.2
Multiply by .
Step 4.2.1.1.4
Move the negative in front of the fraction.
Step 4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.2.1.3.1
Multiply by .
Step 4.2.1.3.2
Multiply by .
Step 4.2.1.4
Combine the numerators over the common denominator.
Step 4.2.1.5
Simplify the numerator.
Step 4.2.1.5.1
Multiply by .
Step 4.2.1.5.2
Subtract from .
Step 4.2.1.6
Simplify each term.
Step 4.2.1.6.1
Cancel the common factor of and .
Step 4.2.1.6.1.1
Factor out of .
Step 4.2.1.6.1.2
Cancel the common factors.
Step 4.2.1.6.1.2.1
Factor out of .
Step 4.2.1.6.1.2.2
Cancel the common factor.
Step 4.2.1.6.1.2.3
Rewrite the expression.
Step 4.2.1.6.2
Move the negative in front of the fraction.
Step 4.2.1.7
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.8
Combine and .
Step 4.2.1.9
Combine the numerators over the common denominator.
Step 4.2.1.10
Combine the numerators over the common denominator.
Step 4.2.1.11
Multiply by .
Step 4.2.1.12
Subtract from .
Step 4.2.1.13
Factor out of .
Step 4.2.1.13.1
Factor out of .
Step 4.2.1.13.2
Factor out of .
Step 4.2.1.13.3
Factor out of .
Step 4.2.1.14
Rewrite as .
Step 4.2.1.15
Factor out of .
Step 4.2.1.16
Factor out of .
Step 4.2.1.17
Move the negative in front of the fraction.
Step 4.3
Replace all occurrences of in with .
Step 4.4
Simplify the right side.
Step 4.4.1
Simplify .
Step 4.4.1.1
Combine the numerators over the common denominator.
Step 4.4.1.2
Simplify each term.
Step 4.4.1.2.1
Apply the distributive property.
Step 4.4.1.2.2
Multiply .
Step 4.4.1.2.2.1
Multiply by .
Step 4.4.1.2.2.2
Combine and .
Step 4.4.1.2.2.3
Multiply by .
Step 4.4.1.2.3
Multiply .
Step 4.4.1.2.3.1
Combine and .
Step 4.4.1.2.3.2
Multiply by .
Step 4.4.1.2.4
Move the negative in front of the fraction.
Step 4.4.1.3
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.4
Simplify terms.
Step 4.4.1.4.1
Combine and .
Step 4.4.1.4.2
Combine the numerators over the common denominator.
Step 4.4.1.5
Simplify the numerator.
Step 4.4.1.5.1
Factor out of .
Step 4.4.1.5.1.1
Factor out of .
Step 4.4.1.5.1.2
Factor out of .
Step 4.4.1.5.1.3
Factor out of .
Step 4.4.1.5.2
Add and .
Step 4.4.1.5.3
Multiply by .
Step 4.4.1.6
Simplify each term.
Step 4.4.1.6.1
Simplify the numerator.
Step 4.4.1.6.1.1
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.6.1.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.4.1.6.1.2.1
Multiply by .
Step 4.4.1.6.1.2.2
Multiply by .
Step 4.4.1.6.1.3
Combine the numerators over the common denominator.
Step 4.4.1.6.1.4
Simplify the numerator.
Step 4.4.1.6.1.4.1
Factor out of .
Step 4.4.1.6.1.4.1.1
Factor out of .
Step 4.4.1.6.1.4.1.2
Factor out of .
Step 4.4.1.6.1.4.1.3
Factor out of .
Step 4.4.1.6.1.4.2
Multiply by .
Step 4.4.1.6.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.4.1.6.3
Multiply .
Step 4.4.1.6.3.1
Multiply by .
Step 4.4.1.6.3.2
Multiply by .
Step 4.4.1.7
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.8
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 4.4.1.8.1
Multiply by .
Step 4.4.1.8.2
Multiply by .
Step 4.4.1.9
Combine the numerators over the common denominator.
Step 4.4.1.10
Simplify the numerator.
Step 4.4.1.10.1
Multiply by .
Step 4.4.1.10.2
Apply the distributive property.
Step 4.4.1.10.3
Multiply by .
Step 4.4.1.10.4
Multiply by .
Step 4.4.1.10.5
Subtract from .
Step 5
Step 5.1
Set the numerator equal to zero.
Step 5.2
Solve the equation for .
Step 5.2.1
Divide each term in by and simplify.
Step 5.2.1.1
Divide each term in by .
Step 5.2.1.2
Simplify the left side.
Step 5.2.1.2.1
Cancel the common factor of .
Step 5.2.1.2.1.1
Cancel the common factor.
Step 5.2.1.2.1.2
Divide by .
Step 5.2.1.3
Simplify the right side.
Step 5.2.1.3.1
Divide by .
Step 5.2.2
Subtract from both sides of the equation.
Step 5.2.3
Divide each term in by and simplify.
Step 5.2.3.1
Divide each term in by .
Step 5.2.3.2
Simplify the left side.
Step 5.2.3.2.1
Cancel the common factor of .
Step 5.2.3.2.1.1
Cancel the common factor.
Step 5.2.3.2.1.2
Divide by .
Step 5.2.3.3
Simplify the right side.
Step 5.2.3.3.1
Dividing two negative values results in a positive value.
Step 6
Step 6.1
Replace all occurrences of in with .
Step 6.2
Simplify the right side.
Step 6.2.1
Simplify .
Step 6.2.1.1
Simplify the numerator.
Step 6.2.1.1.1
Cancel the common factor of .
Step 6.2.1.1.1.1
Factor out of .
Step 6.2.1.1.1.2
Factor out of .
Step 6.2.1.1.1.3
Cancel the common factor.
Step 6.2.1.1.1.4
Rewrite the expression.
Step 6.2.1.1.2
Combine and .
Step 6.2.1.1.3
Multiply by .
Step 6.2.1.1.4
To write as a fraction with a common denominator, multiply by .
Step 6.2.1.1.5
Combine and .
Step 6.2.1.1.6
Combine the numerators over the common denominator.
Step 6.2.1.1.7
Simplify the numerator.
Step 6.2.1.1.7.1
Multiply by .
Step 6.2.1.1.7.2
Add and .
Step 6.2.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 6.2.1.3
Cancel the common factor of .
Step 6.2.1.3.1
Factor out of .
Step 6.2.1.3.2
Factor out of .
Step 6.2.1.3.3
Cancel the common factor.
Step 6.2.1.3.4
Rewrite the expression.
Step 6.2.1.4
Multiply by .
Step 6.2.1.5
Multiply by .
Step 6.3
Replace all occurrences of in with .
Step 6.4
Simplify the right side.
Step 6.4.1
Simplify .
Step 6.4.1.1
Simplify each term.
Step 6.4.1.1.1
Combine and .
Step 6.4.1.1.2
Multiply by .
Step 6.4.1.1.3
Multiply the numerator by the reciprocal of the denominator.
Step 6.4.1.1.4
Multiply .
Step 6.4.1.1.4.1
Multiply by .
Step 6.4.1.1.4.2
Multiply by .
Step 6.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 6.4.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 6.4.1.3.1
Multiply by .
Step 6.4.1.3.2
Multiply by .
Step 6.4.1.4
Combine the numerators over the common denominator.
Step 6.4.1.5
Simplify the numerator.
Step 6.4.1.5.1
Multiply by .
Step 6.4.1.5.2
Add and .
Step 6.4.1.6
Cancel the common factor of and .
Step 6.4.1.6.1
Factor out of .
Step 6.4.1.6.2
Cancel the common factors.
Step 6.4.1.6.2.1
Factor out of .
Step 6.4.1.6.2.2
Cancel the common factor.
Step 6.4.1.6.2.3
Rewrite the expression.
Step 7
List all of the solutions.