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Solving Rational Equations & Proportions in Algebra 2

Learn to solve rational equations and proportions in algebra utilizing proportions & fractions. Practice with real-life examples. Identify extraneous solutions. Find the LCM to simplify equations. Includes assignments for clarity.

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Solving Rational Equations & Proportions in Algebra 2

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  1. Honors Algebra 2 Section 7.5 Solving Rational Equations

  2. Rational equations that have one term on each side of the equal sign form a proportion and can be solved as a proportion. • How do you solve for a variable in a proportion?

  3. What is important to do before cross multiplying?

  4. Solve for x. • There can be extraneous solutions! You just need to check that none of the answers would result in a zero in the denominator in the original equation.

  5. Real-life • White gold is an alloy (mixture of metals) composed of 75% gold and 25% palladium by weight. You have 12 ounces of an alloy that is 60% gold and 40% palladium. How much pure gold should you mix with this alloy to make white gold? • What does the variable represent?

  6. Let x= amount of pure gold to add to the alloy • How many ounces of palladium is there in 12 ounces of the present alloy? • Will adding pure gold decrease or increase the percent of palladium in the alloy?

  7. What percent of palladium do we want to make white gold? • What is the proportion?

  8. How is x labeled?

  9. Rational equations that have more than one term on either side of the equal sign can be solved by multiplying through by the LCM to eliminate all the fractions.

  10. Find the LCM of the following #1 #2 #3 #4

  11. Solve for x. #1 #2 Don’t forget to check for extraneous roots.

  12. When the numerators have more than one term, use parentheses!

  13. Assignment #33 Pg. 396 #1,2, 3-33 odd

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