Precalculus Examples

Move all terms not containing to the right side of the equation.
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Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Simplify the right side of the equation.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by to get .
Add and to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
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Factor out of .
Factor out of .
Move .
Multiply by to get .
Cancel the common factor.
Rewrite the expression.
Set up the rational expression with the same denominator over the entire equation.
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Multiply each term by a factor of that will equate all the denominators. In this case, all terms need a denominator of . The expression needs to be multiplied by to make the denominator . The expression needs to be multiplied by to make the denominator .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
Multiply by to get .
Multiply the expression by a factor of to create the least common denominator (LCD) of .
Multiply by to get .
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Rewrite the equation as .
Multiply by to get .
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Check that all solutions found are valid and are part of the domain by substituting them into the original equation.
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