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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
Subtract from 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
Divide by .
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 1.2.3.1.2.2.4
Divide by .
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
Multiply by .
Step 2.2.1.1.2.2
Multiply .
Step 2.2.1.1.2.2.1
Combine and .
Step 2.2.1.1.2.2.2
Multiply by .
Step 2.2.1.1.2.3
Multiply by .
Step 2.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.3
Simplify terms.
Step 2.2.1.3.1
Combine and .
Step 2.2.1.3.2
Combine the numerators over the common denominator.
Step 2.2.1.4
Simplify each term.
Step 2.2.1.4.1
Simplify the numerator.
Step 2.2.1.4.1.1
Factor out of .
Step 2.2.1.4.1.1.1
Factor out of .
Step 2.2.1.4.1.1.2
Factor out of .
Step 2.2.1.4.1.1.3
Factor out of .
Step 2.2.1.4.1.2
Multiply by .
Step 2.2.1.4.1.3
Add and .
Step 2.2.1.4.2
Move to the left of .
Step 2.2.1.5
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
Multiply by .
Step 2.4.1.1.2.2
Multiply .
Step 2.4.1.1.2.2.1
Combine and .
Step 2.4.1.1.2.2.2
Multiply by .
Step 2.4.1.1.2.3
Multiply by .
Step 2.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.4.1.3
Simplify terms.
Step 2.4.1.3.1
Combine and .
Step 2.4.1.3.2
Combine the numerators over the common denominator.
Step 2.4.1.4
Simplify each term.
Step 2.4.1.4.1
Simplify the numerator.
Step 2.4.1.4.1.1
Factor out of .
Step 2.4.1.4.1.1.1
Factor out of .
Step 2.4.1.4.1.1.2
Factor out of .
Step 2.4.1.4.1.1.3
Factor out of .
Step 2.4.1.4.1.2
Multiply by .
Step 2.4.1.4.1.3
Add and .
Step 2.4.1.4.2
Move to the left of .
Step 2.4.1.5
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
Subtract from both sides of the equation.
Step 3.1.3
Subtract from .
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
Dividing two negative values results in a positive value.
Step 3.2.3.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.2.3.1.3
Move the negative in front of the fraction.
Step 3.2.3.1.4
Multiply .
Step 3.2.3.1.4.1
Multiply by .
Step 3.2.3.1.4.2
Multiply by .
Step 3.2.3.1.4.3
Multiply by .
Step 3.2.3.1.4.4
Multiply 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
Find the common denominator.
Step 4.2.1.1.1
Write as a fraction with denominator .
Step 4.2.1.1.2
Multiply by .
Step 4.2.1.1.3
Multiply by .
Step 4.2.1.1.4
Write as a fraction with denominator .
Step 4.2.1.1.5
Multiply by .
Step 4.2.1.1.6
Multiply by .
Step 4.2.1.2
Combine the numerators over the common denominator.
Step 4.2.1.3
Simplify each term.
Step 4.2.1.3.1
Multiply by .
Step 4.2.1.3.2
Apply the distributive property.
Step 4.2.1.3.3
Multiply .
Step 4.2.1.3.3.1
Combine and .
Step 4.2.1.3.3.2
Multiply by .
Step 4.2.1.3.4
Multiply .
Step 4.2.1.3.4.1
Combine and .
Step 4.2.1.3.4.2
Multiply by .
Step 4.2.1.3.5
Simplify each term.
Step 4.2.1.3.5.1
Move the negative in front of the fraction.
Step 4.2.1.3.5.2
Move the negative in front of the fraction.
Step 4.2.1.3.6
Apply the distributive property.
Step 4.2.1.3.7
Multiply .
Step 4.2.1.3.7.1
Multiply by .
Step 4.2.1.3.7.2
Combine and .
Step 4.2.1.3.7.3
Multiply by .
Step 4.2.1.3.8
Cancel the common factor of .
Step 4.2.1.3.8.1
Move the leading negative in into the numerator.
Step 4.2.1.3.8.2
Factor out of .
Step 4.2.1.3.8.3
Cancel the common factor.
Step 4.2.1.3.8.4
Rewrite the expression.
Step 4.2.1.3.9
Simplify each term.
Step 4.2.1.3.9.1
Move the negative in front of the fraction.
Step 4.2.1.3.9.2
Move the negative in front of the fraction.
Step 4.2.1.4
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.5
Combine and .
Step 4.2.1.6
Combine the numerators over the common denominator.
Step 4.2.1.7
Simplify the numerator.
Step 4.2.1.7.1
Multiply by .
Step 4.2.1.7.2
Subtract from .
Step 4.2.1.8
Move the negative in front of the fraction.
Step 4.2.1.9
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.10
Combine and .
Step 4.2.1.11
Combine the numerators over the common denominator.
Step 4.2.1.12
Combine the numerators over the common denominator.
Step 4.2.1.13
Multiply by .
Step 4.2.1.14
Add and .
Step 4.2.1.15
Factor out of .
Step 4.2.1.15.1
Factor out of .
Step 4.2.1.15.2
Factor out of .
Step 4.2.1.15.3
Factor out of .
Step 4.2.1.16
Rewrite as .
Step 4.2.1.17
Factor out of .
Step 4.2.1.18
Factor out of .
Step 4.2.1.19
Move the negative in front of the fraction.
Step 4.2.1.20
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.1.21
Cancel the common factor of .
Step 4.2.1.21.1
Move the leading negative in into the numerator.
Step 4.2.1.21.2
Factor out of .
Step 4.2.1.21.3
Cancel the common factor.
Step 4.2.1.21.4
Rewrite the expression.
Step 4.2.1.22
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
Cancel the common factor of .
Step 4.4.1.1.2.1
Factor out of .
Step 4.4.1.1.2.2
Factor out of .
Step 4.4.1.1.2.3
Cancel the common factor.
Step 4.4.1.1.2.4
Rewrite the expression.
Step 4.4.1.1.3
Cancel the common factor of .
Step 4.4.1.1.3.1
Factor out of .
Step 4.4.1.1.3.2
Factor out of .
Step 4.4.1.1.3.3
Cancel the common factor.
Step 4.4.1.1.3.4
Rewrite the expression.
Step 4.4.1.1.4
Simplify each term.
Step 4.4.1.1.4.1
Rewrite as .
Step 4.4.1.1.4.2
Rewrite as .
Step 4.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.4.1.3
Combine and .
Step 4.4.1.4
Combine the numerators over the common denominator.
Step 4.4.1.5
Simplify the numerator.
Step 4.4.1.5.1
Multiply by .
Step 4.4.1.5.2
Subtract from .
Step 4.4.1.6
Move the negative in front of the fraction.
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 each term.
Step 4.4.1.10.1
Simplify the numerator.
Step 4.4.1.10.1.1
Factor out of .
Step 4.4.1.10.1.1.1
Factor out of .
Step 4.4.1.10.1.1.2
Factor out of .
Step 4.4.1.10.1.1.3
Factor out of .
Step 4.4.1.10.1.2
Multiply by .
Step 4.4.1.10.1.3
Subtract from .
Step 4.4.1.10.2
Move to the left of .
Step 4.4.1.10.3
Move the negative in front of the fraction.
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
Factor out of .
Step 5.2.1.1.1.3
Cancel the common factor.
Step 5.2.1.1.1.4
Rewrite the expression.
Step 5.2.1.1.2
Multiply.
Step 5.2.1.1.2.1
Multiply by .
Step 5.2.1.1.2.2
Multiply by .
Step 5.2.2
Simplify the right side.
Step 5.2.2.1
Multiply by .
Step 5.3
Move all terms not containing to the right side of the equation.
Step 5.3.1
Subtract from both sides of the equation.
Step 5.3.2
Subtract from .
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
Simplify each term.
Step 6.2.1.1.1
Cancel the common factor of and .
Step 6.2.1.1.1.1
Factor out of .
Step 6.2.1.1.1.2
Cancel the common factors.
Step 6.2.1.1.1.2.1
Factor out of .
Step 6.2.1.1.1.2.2
Cancel the common factor.
Step 6.2.1.1.1.2.3
Rewrite the expression.
Step 6.2.1.1.2
Multiply by .
Step 6.2.1.1.3
Move the negative in front of the fraction.
Step 6.2.1.1.4
Multiply .
Step 6.2.1.1.4.1
Multiply by .
Step 6.2.1.1.4.2
Multiply by .
Step 6.2.1.2
Combine fractions.
Step 6.2.1.2.1
Combine the numerators over the common denominator.
Step 6.2.1.2.2
Simplify the expression.
Step 6.2.1.2.2.1
Subtract from .
Step 6.2.1.2.2.2
Divide 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
Multiply by .
Step 6.4.1.2
Simplify each term.
Step 6.4.1.2.1
Cancel the common factor of and .
Step 6.4.1.2.1.1
Factor out of .
Step 6.4.1.2.1.2
Cancel the common factors.
Step 6.4.1.2.1.2.1
Factor out of .
Step 6.4.1.2.1.2.2
Cancel the common factor.
Step 6.4.1.2.1.2.3
Rewrite the expression.
Step 6.4.1.2.2
Move the negative in front of the fraction.
Step 6.4.1.3
Combine fractions.
Step 6.4.1.3.1
Combine the numerators over the common denominator.
Step 6.4.1.3.2
Simplify the expression.
Step 6.4.1.3.2.1
Subtract from .
Step 6.4.1.3.2.2
Divide by .
Step 7
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 8
The result can be shown in multiple forms.
Point Form:
Equation Form: