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Math 117: Test 2 Jennifer Riddell Section 5.1 Exercise 40 Write each expression in simplest form. = 3(a 4) 3(4 a) 3 (4 a)( 4 a) (4 a)( 4 a) 4 a Section 5.2 Exercise 40 Divide the following fractions. = Factor each one: r2 +2rs -15s2 = (r-3s) (r+5s) r3 +5r2s = r2(r+5s) r2 -9s2 = (r-3s) (r+3s) Flip the second and multiply: (r-3s)(r+5s)/(r^2)(r+5s) * 5r^3 / (r-3s)(r+3s) = 1/(r^2) * 5r^3 /(r+3s) = 5r/(r+3s) Section 5.3 Exercise 40 Add or subtract as indicated. Express your results in simplest form. = 2 x 6 2( x 3) 2 x3 x3 Section 5.4 Exercise 60 Add or subtract as indicated. Express your result in simplest form. = Factor the bottoms: 2a/(a-4)(a+3) – 3/(a-4)(a+2) Common denom: 2a(a+2)/CD – 3(a+3)/CD, where CD = (a-4)(a+3)(a+2) Subtract: (2a(a+2) – 3(a+3))/CD = (2a^2 + 4a – 3a – 9) / CD = (2a^2 + a – 9) / CD = (2a^2 + a – 9) / (a-4)(a+3)(a+2) Section 5.5 Exercise 60 Solve and check each of the following equations for x. Factor the second term: 5x/(x-4)(x+3) Make everything get a common denom: X(x+3)/CD = 5x/CD – 3(x-4)/CD Multiply by CD: X(x+3) = 5x – 3(x-4) X^2 + 3x = 5x – 3x + 12 Combine: X^2 + x –12 = 0 Factor: (x-3)(x+4) = 0 x = 3 or –4 Check: 3/(3-4) = 3/-1 (5*3)/(3^2-3-12)-3/(3+3) = -3 Check: -4/(-4-4) = 0.5 (5*-4)/(-4^2-(-4)-12) – 3/(-4+3) = 0.5 x = 3 or -4 Exercise 70 Solve the equation for x. = Factors 9 and 30 have greatest common factor of 3. Reducing fraction. It becomes x 3 10 10 Move these terms to the left - It now becomes 3 10 x 3 0 10 10 Solved linear equation x 3 0 equivalent to 0.1·x-0.3=0 10 10 Solution x=3 Section 5.6 Exercise 20 Science and medicine. A small business jet took 1 h longer to fly 810 mi on the first part of a flight than to fly 540 mi on the second portion. If the jet’s rate was the same for each leg of the flight, what was the flying time for each leg? In 1 hour, they went 810-540 miles = 270 miles Therefore the times were: 540/270 = 2 hours and 810/270 = 3 hours Exercise 30 Business and finance. If 342 cups of coffee can be made from 9 lb of coffee, how many cups can be made from 6 lb of coffee? Proportion: 342/9 = x/6 Cross multiply: 9x = 6*342 x = 6*342/9 x = 228 cups Section 5.7 Exercise 20 Simplify each complex fraction. Get common denoms (xy): 1/xy + 2y/xy __________ 3x/xy – 1/xy Combine: (1+2y)/xy __________ (3x-1)/xy Remove the xy: (1+2y)/(3x-1) Exercise 30 Take the area divided by the length: Flip the length and multiply: 2(3x-2)/(x-1) * (x-2)/(3x-2) Cancel: 2/(x-1) * (x-2) = 2(x-2)/(x-1)