# Precalculus Examples

Subtract from both sides of the equation.

Simplify the right side of the equation.

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 .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Add and .

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 .

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Verify each of the solutions by substituting them into and solving.