Solve the following equations. 

1. -1 1 1 1 = 4 (r+ 21)(r+ 23) +...+ (r+1)(x+3) (r+3)(x +5) ' (r+ 5)(x +7) 2. 1 1 1 1 (r+2)(r+ 4) (r+ 4)(r+6) (r+6)(x+8) = 5 (r+24)(r + 26) 3. 1 1 1 1 +...+ (r+1)(r+4) (r+4)(r+7) (r+7)(r +10) = 6 (I+25)(x+28) 4. 1 1 1 1 = 7 (r+28)(r+31) +...+ (r +2)(x +5) (r+5)(r+8) (r+8)(r+10) 5. 1 1 1 8. (I+30)(x +33) +...+ (*+3) ( + 6) (+6)(z +9) 6. 1 1 1 (2x+1)(2r + 3) (2r+3)(2r+5) (2r+5)(2r+ 7) (2x+25)(2x+27) 7. 1 1 = 10 (3x+1)(3x+4) (3x+4)(3x +7) (3r+ 7)(3r+ 10) +...+ (3x+31)(3r+ 34) 8. 1 1 1 + (4x +3)(4x +7) (4x+7)(4r +11) (4x +11)(4.x + 15) 11 (4.x+23)(4r+ 27) 9. 1 1 1 1 (5x+12)(5x+ 17) = 12 (5x +27)(5x + 32) (5x +2)(5r +7) (5x + 7)(5r +12) 10. 1 1 1 +...+ = 13 (6x + 1)(6r +7) (6x+7)(6r+13) (6r +13)(6r+ 19) (6x + 37)(6x+ 43) fraction decomposition