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Finite Math Examples
, ,
Step 1
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
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
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 2.2.1.2.1
Multiply by .
Step 2.2.1.2.2
Multiply by .
Step 2.2.1.3
Combine the numerators over the common denominator.
Step 2.2.1.4
Add and .
Step 2.2.1.4.1
Reorder and .
Step 2.2.1.4.2
Add and .
Step 2.2.1.5
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.6
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.7
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 2.2.1.7.1
Multiply by .
Step 2.2.1.7.2
Multiply by .
Step 2.2.1.7.3
Multiply by .
Step 2.2.1.7.4
Multiply by .
Step 2.2.1.8
Combine the numerators over the common denominator.
Step 2.2.1.9
Simplify the numerator.
Step 2.2.1.9.1
Apply the distributive property.
Step 2.2.1.9.2
Simplify.
Step 2.2.1.9.2.1
Multiply by .
Step 2.2.1.9.2.2
Move to the left of .
Step 2.2.1.9.2.3
Multiply by .
Step 2.2.1.9.3
Move to the left of .
Step 2.2.1.9.4
Add and .
Step 3
Step 3.1
Move all terms not containing to the right side of the equation.
Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Add to 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
Move the negative in front of the fraction.
Step 3.2.3.1.2
Divide by .
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 the numerator.
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 by .
Step 4.2.1.1.4
Move the negative in front of the fraction.
Step 4.2.1.1.5
Add and .
Step 4.2.1.1.6
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.1.7
Combine and .
Step 4.2.1.1.8
Combine the numerators over the common denominator.
Step 4.2.1.1.9
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.1.10
Combine and .
Step 4.2.1.1.11
Combine the numerators over the common denominator.
Step 4.2.1.1.12
Rewrite in a factored form.
Step 4.2.1.1.12.1
Multiply by .
Step 4.2.1.1.12.2
Multiply by .
Step 4.2.1.1.12.3
Subtract from .
Step 4.2.1.1.12.4
Factor out of .
Step 4.2.1.1.12.4.1
Factor out of .
Step 4.2.1.1.12.4.2
Factor out of .
Step 4.2.1.1.12.4.3
Factor out of .
Step 4.2.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.1.3
Multiply .
Step 4.2.1.3.1
Multiply by .
Step 4.2.1.3.2
Multiply by .
Step 4.2.1.4
Factor out of .
Step 4.2.1.5
Rewrite as .
Step 4.2.1.6
Factor out of .
Step 4.2.1.7
Simplify the expression.
Step 4.2.1.7.1
Rewrite as .
Step 4.2.1.7.2
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
Simplify each term.
Step 4.4.1.1.1
Apply the distributive property.
Step 4.4.1.1.2
Multiply .
Step 4.4.1.1.2.1
Multiply by .
Step 4.4.1.1.2.2
Multiply by .
Step 4.4.1.1.3
Multiply by .
Step 4.4.1.2
Subtract from .
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 each term.
Step 4.4.1.5.1
Simplify the numerator.
Step 4.4.1.5.1.1
Factor out of .
Step 4.4.1.5.1.1.1
Factor out of .
Step 4.4.1.5.1.1.2
Factor out of .
Step 4.4.1.5.1.1.3
Factor out of .
Step 4.4.1.5.1.2
Multiply by .
Step 4.4.1.5.1.3
Subtract from .
Step 4.4.1.5.2
Move to the left of .
Step 5
Step 5.1
Multiply both sides of the equation by .
Step 5.2
Simplify both sides of the equation.
Step 5.2.1
Simplify the left side.
Step 5.2.1.1
Simplify .
Step 5.2.1.1.1
Cancel the common factor of .
Step 5.2.1.1.1.1
Move the leading negative in into the numerator.
Step 5.2.1.1.1.2
Move the leading negative in into the numerator.
Step 5.2.1.1.1.3
Factor out of .
Step 5.2.1.1.1.4
Cancel the common factor.
Step 5.2.1.1.1.5
Rewrite the expression.
Step 5.2.1.1.2
Cancel the common factor of .
Step 5.2.1.1.2.1
Factor out of .
Step 5.2.1.1.2.2
Cancel the common factor.
Step 5.2.1.1.2.3
Rewrite the expression.
Step 5.2.1.1.3
Multiply.
Step 5.2.1.1.3.1
Multiply by .
Step 5.2.1.1.3.2
Multiply by .
Step 5.2.2
Simplify the right side.
Step 5.2.2.1
Simplify .
Step 5.2.2.1.1
Cancel the common factor of .
Step 5.2.2.1.1.1
Move the leading negative in into the numerator.
Step 5.2.2.1.1.2
Factor out of .
Step 5.2.2.1.1.3
Cancel the common factor.
Step 5.2.2.1.1.4
Rewrite the expression.
Step 5.2.2.1.2
Multiply by .
Step 5.3
Move all terms not containing to the right side of the equation.
Step 5.3.1
Add to both sides of the equation.
Step 5.3.2
Add and .
Step 5.4
Divide each term in by and simplify.
Step 5.4.1
Divide each term in by .
Step 5.4.2
Simplify the left side.
Step 5.4.2.1
Cancel the common factor of .
Step 5.4.2.1.1
Cancel the common factor.
Step 5.4.2.1.2
Divide by .
Step 5.4.3
Simplify the right side.
Step 5.4.3.1
Divide by .
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
Multiply by .
Step 6.2.1.2
Divide by .
Step 6.2.1.3
Subtract from .
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
Cancel the common factor of and .
Step 6.4.1.1.1.1
Factor out of .
Step 6.4.1.1.1.2
Cancel the common factors.
Step 6.4.1.1.1.2.1
Factor out of .
Step 6.4.1.1.1.2.2
Cancel the common factor.
Step 6.4.1.1.1.2.3
Rewrite the expression.
Step 6.4.1.1.1.2.4
Divide by .
Step 6.4.1.1.2
Multiply .
Step 6.4.1.1.2.1
Multiply by .
Step 6.4.1.1.2.2
Multiply by .
Step 6.4.1.2
Add and .
Step 7
List all of the solutions.