Add or subtract.

25. 7 3 a + 2 5 fraction 7 , over 3 eh end fraction , plus , 2 fifths
26. 4 x − 2 3 4 over x , minus , 2 thirds
27. 27 n 3 − 9 7 n 2 fraction 27 , over n cubed end fraction , minus . fraction 9 , over 7 , n squared end fraction
28. 6 5 x 8 + 4 3 x 6 fraction 6 , over 5 , x to the eighth end fraction . plus . fraction 4 , over 3 , x to the sixth end fraction
29. a a + 3 − 4 a + 5 fraction eh , over eh plus 3 end fraction . minus . fraction 4 , over eh plus 5 end fraction
30. 9 m + 2 + 8 m − 7 fraction 9 , over m plus 2 end fraction . plus . fraction 8 , over m minus 7 end fraction
31. a a + 3 + a + 5 4 fraction eh , over eh plus 3 end fraction . plus . fraction eh plus 5 , over 4 end fraction
32. 5 t 2 − 4 t + 1 fraction 5 , over t squared end fraction , minus . fraction 4 , over t plus 1 end fraction

See Problem 5.

33. Exercise Jane walks one mile from her house to her grandparents' house. Then she returns home, walking with her grandfather. Her return rate is 70% of her rate walking alone. Let r represent her rate walking alone.
    1. Write an expression for the amount of time Jane spends walking.
    2. Simplify your expression.
    3. Suppose Jane's rate walking alone is 3 mi/h. About how much time does she spend walking?

B Apply

34. Error Analysis A student added two rational expressions as shown. What error did the student make?

    

35. Writing When you use the LCD to add or subtract rational expressions, will the answer always be in simplest form if you use the LCD? Explain.
36. Open-Ended Write two rational expressions with different denominators. Find the LCD and add the two expressions.

Add or subtract.

37. y 2 + 2 y − 1 3 y + 1 − 2 y 2 − 3 3 y + 1 fraction y squared , plus 2 y minus 1 , over 3 y plus 1 end fraction . minus . fraction 2 , y squared , minus 3 , over 3 y plus 1 end fraction
38. h 2 + 1 2 t 2 − 7 + h 2 t 2 − 7 fraction h squared , plus 1 , over 2 , t squared , minus 7 end fraction . plus . fraction h , over 2 , t squared , minus 7 end fraction
39. r − 5 9 + p 3 − 2 k + 1 9 + p 3 fraction r minus 5 , over 9 plus , p cubed end fraction . minus . fraction 2 k plus 1 , over 9 plus , p cubed end fraction
40. 2 − x x y 2 z − 5 + z x y 2 z fraction 2 minus x , over x , y squared , z end fraction . minus . fraction 5 plus z , over x , y squared , z end fraction
41. 9 + x − 3 x + 2 9 plus . fraction x minus 3 , over x plus 2 end fraction
42. t 2 t − 3 − 11 fraction t , over 2 t minus 3 end fraction . minus 11
43. Think About a Plan The groundspeed for jet traffic from Los Angeles to New York City can be about 100 mi/h faster than the groundspeed from New York City to Los Angeles. This difference is due to a strong westerly wind at high altitudes. If r is a jet's groundspeed from New York City to Los Angeles, write and simplify an expression for the round-trip air time. The two cities are about 2500 mi apart.
    • Can you write an expression for the air time from New York City to Los Angeles?
    • In terms of r, what is the jet's groundspeed from Los Angeles to New York City? Can you use this speed to write an expression for the air time from Los Angeles to New York City?
44. Rowing A rowing team practices rowing 2 mi upstream and 2 mi downstream. The team can row downstream 25% faster than they can row upstream.
    1. Let u represent the team's rate rowing upstream. Write and simplify an expression involving u for the total amount of time they spend rowing.
    2. Let d represent the team's rate rowing downstream. Write and simplify an expression involving d for the total amount of time they spend rowing.
    3. Reasoning Do the expressions you wrote in parts (a) and (b) represent the same time? Explain.

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