Outro W11

8.5 Simplify Complex Rational Expressions

• To Simplify a Rational Expression by Writing it as Division
  1. Step 1. Simplify the numerator and denominator.
  2. Step 2. Rewrite the complex rational expression as a division problem.
  3. Step 3. Divide the expressions.
• To Simplify a Complex Rational Expression by Using the LCD
  1. Step 1. Find the LCD of all fractions in the complex rational expression.
  2. Step 2. Multiply the numerator and denominator by the LCD.
  3. Step 3. Simplify the expression.

8.6 Solve Rational Equations

• Strategy to Solve Equations with Rational Expressions
  1. Step 1. Note any value of the variable that would make any denominator zero.
  2. Step 2. Find the least common denominator of all denominators in the equation.
  3. Step 3. Clear the fractions by multiplying both sides of the equation by the LCD.
  4. Step 4. Solve the resulting equation.
  5. Step 5. Check.
  • If any values found in Step 1 are algebraic solutions, discard them.
  • Check any remaining solutions in the original equation.

8.7 Solve Proportion and Similar Figure Applications

• Property of Similar Triangles
  • If ΔABC$\text{Δ}ABC$ is similar to ΔXYZ$\text{Δ}XYZ$, then their corresponding angle measures are equal and their corresponding sides are in the same ratio.
• Problem Solving Strategy for Geometry Applications
  1. Step 1. Read the problem and make sure all the words and ideas are understood. Draw the figure and label it with the given information.
  2. Step 2. Identify what we are looking for.
  3. Step 3. Name what we are looking for by choosing a variable to represent it.
  4. Step 4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
  5. Step 5. Solve the equation using good algebra techniques.
  6. Step 6. Check the answer in the problem and make sure it makes sense.
  7. Step 7. Answer the question with a complete sentence