Answer Happy

Practice Exercises In Exercises 1-16, perform the indicated operations. These exercises involve addition and subtraction when denominators are the same. Simplify the result, if possible. 1. 9x2​+9x4​ 2. 6x11​+6x4​ 3. x−5x​+x−59x+3​ 4. x−3x​+x−311x+5​ 5. x2+3xx2−2x​+x2+3xx2+x​ 6. x2−5xx2+7x​+x2−5xx2−4x​ 7. y2−9y2​+y2−99−6y​
11. x2+6x−7x2−2​−x2+6x−719−4x​
In Exercises 17-28, find the least common denominator of the rational expressions. 17. 25x211​ and 35x14​ 18. 15x27​ and 24x9​ 19. x−52​ and x2−253​ 20. x+32​ and x2−95​ 21. y2−1007​ and y(y−10)13​ 22. y2−47​ and y(y+2)15​ 23. x2−168​ and x2−8x+16x​ 24. x2−253​ and x2−10x+25x​ 25. y2−5y−67​ and y2−4y−5y​
In Exercises 29-66, perform the indicated operations. These exercises involve addition and subtraction when denominators are different. Simplify the result, if possible. 29. 5x23​+x10​ 30. 2x27​+x4​ 31. x−24​+x+13​ 32. x−32​+x+27​ 33. x2+x−23x​+x2−4x+32​ 34. x2+2x−87x​+x2−3x+23​ 35. x+5x−6​+x−6x+5​ 36. x+7x−2​+x−2x+7​ 37. x2−253x​−x+54​
43. x2+7x+124x+1​+x2+5x+42x+3​
53. x−42x​+x2−1664​−x+42x​
57. 5x+63​−x−24​+5x2−4x−12x2−x​
Practice Exercises In Exercises 1-40, simplify each complex rational expression by the method of your choice. 1. 1−x3​4+x2​​ 2. 3+x1​5−x2​​ 3. 3x​−x3​x3​+3x​​ 4. 51​+x1​5x​−x5​​ 5. x1​−y1​x1​+y1​​ 6. xy​+x1​yx​+x1​​ 7. 10x−1−6x−28x−2−2x−1​ 8. 15x−1−9x−212x−2−3x−1​ 9. 1−x−21​x−21​​ 10. 1+x+21​x+21​​
x3y5​−xy3​x3y2​+xy45​​
29. y+31​+y+12​y2+4y+32y​​
In Exercises 47-48, let f(x)=1−x1+x​. 47. Find f(x+31​) and simplify. 48. Find f(x−61​) and simplify. In Exercises 49-50, use the given rational function to find and simplify hf(a+h)−f(a)​ 49. f(x)=x3​