Chapter 11 - Crestwood Local School District

1A._ 15 y 24x1C._ b + 43b + 2÷ _ 5y8 x 3÷ _ 3b + 12b + 1Find each quotient.1B._ 27 c 3 d 211d1D._ 6b - 123b + 15÷ _ 2 c 39 d 3 e÷ _ 12b + 18b + 5Sometimes you must factor a quadratic expression before you can simplify thequotient of rational expressions.EXAMPLEFind m __2 + 3m + 242__m + 3m + 24Expression Involving Polynomials÷ _ m + 2÷ _ m + 2m + 1 .__m + 1 = m 2 + 3m + 24===__(m + 1)(m + 2)41(m __+ 1) (m + 2)4(m + 1)2_4·_m + 1m + 2· _ m + 1m + 2· _ m + 1m + 21Multiply by the reciprocal, _ m + 1m + 2 .Factor m 2 + 3m + 2.The GCF is m + 2.Simplify.Find each quotient.2A._ p 2 - 45p÷ _ p - 2p + q2B._q 2 + 3q + 212÷ _ q + 1q 2 + 4DIMENSIONAL ANALYSIS You can divide rational expressions that involveunits of measure by using dimensional analysis.Real-World LinkThe first successful Marsprobe was the Mariner4, which arrived at Marson July 14, 1965.Source: NASASPACE In April, 2001, NASA launched the Mars Odyssey spacecraft. Ittook 200 days for the spacecraft to travel 466,000,000 miles from Earthto Mars. What was the average speed of the spacecraft in miles perhour? Round to the nearest mile per hour.rt = drate · time = distancer · 200 days = 466,000,000 mi t = 200 days, d = 466,000,000r ===__466,000,000 mi200 days__466,000,000 miles·200 days__466,000,000 miles4800 hours1 day _24 hoursDivide each side by 200 days.Convert days to hours.97,083 milesor about __1 hour596 Chapter 11 Rational Expressions and EquationsThus, the spacecraft traveled at a rate of about 97,083 miles per hour.