Section 7.5 Solving Rational Equations Honors Algebra 2 Section 7.5 Solving Rational Equations

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?

What is important to do before cross multiplying?

Solve for x. 2 𝑥+2 = 10 3𝑥+2 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.

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?

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?

𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑝𝑎𝑙𝑙𝑎𝑑𝑖𝑢𝑚 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑖𝑥𝑡𝑢𝑟𝑒= 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑎𝑙𝑙𝑎𝑑𝑖𝑢𝑚 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑖𝑥𝑡𝑢𝑟𝑒 𝑡𝑜𝑡𝑎𝑙 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑚𝑖𝑥𝑡𝑢𝑟𝑒 What percent of palladium do we want to make white gold? What is the proportion?

25 100 = .40(12) 12+𝑥 How is x labeled?

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.

Find the LCM of the following #1 6𝑥 𝑎𝑛𝑑 4𝑥 #2 3𝑥 2 𝑎𝑛𝑑 15𝑥 5 #3 𝑥 2 +2𝑥+1 𝑎𝑛𝑑 𝑥 2 −1 #4 𝑥 2 𝑎𝑛𝑑 𝑥−7

Solve for x. #1 3 𝑥 + 5 2 =− 12 𝑥 #2 1− 2 𝑥−4 = 4 𝑥 Don’t forget to check for extraneous roots.

When the numerators have more than one term, use parentheses! 4𝑥 𝑥 2 −9 = 𝑥−1 𝑥 2 −6𝑥+9 + 2 𝑥+3

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