A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis.

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Solving Rational Equations

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Presentation transcript:

A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis

Domain Recall: The domain is the set of all x values for which an expression exists. Ex. Find the domain of the following expression.

Solving Rational Equations Recall how to solve the following equation…

Steps for Solving Rational Equations Step 1: Factor all denominators completely. Step 2: Determine the least common denominator. Step 3: Multiply both sides by the LCM (distribute!). Step 4: Solve the new polynomial equation using learned methods. Step 5: Check for any extraneous solutions in the original equation.

Solving Rational Equations Solve the equation.

Solving Rational Equations What if we have one a little more tricky?!

Solving Quadratic Equations: GCF Solve the equation.

Completing the Square (a = 1) Step 1: Move c to the other side Step 2: Add to both sides Step 3: Rewrite the left side as the perfect square Step 4: both sides and solve!

Completing the Square (a ≠ 1) Solve the equation.

Equations in Quadratic Form The following equation resembles quadratic form. Let’s solve it!

Equations in Quadratic Form How can we solve this equation without multiplying it out?

Solving Absolute Value Equations What does “absolute value” mean? What is the meaning of this equation?

Steps for Solving Absolute Value Equations Step 1: Isolate absolute value on one side of the equation. Step 2: Rewrite the equation, removing the absolute value, and plus/minus of the other side of the equation. Step 3: Solve each equation for x. Step 4: Check for any extraneous solutions in the original equation.

Solving Absolute Value Equations Solve the following equation for x.

A.5 Methods for Solving Equations Failures are finger posts on the road to achievement. -C. S. Lewis Homework: