求解以下每个方程式，并验证您的解决方案：
问题1： 9(1/4)= y – 1(1/3)
解决方案：
(37 / 4) = y – (4/3)
(37 / 4) + (4 / 3) = y
Calculate LCM of 4 and 3 which is 12.
(((37 * 3) * (4 * 4)) / 12) = y
(111 + 16) / 12 = y
127 / 12 = y
Verification:
Putting y = 127 / 12
RHS = y – (4 / 3)
= 127 / 12 – 4 / 3
Calculate LCM of 12 and 3 which is 12
= (127 – (4 * 4)) / 12
= (127 – 16) / 12
= 111 / 12
Divide it by 3
= 37 / 4
= 9 (1/4)
LHS = RHS
Hence, verified.
问题2： (5x / 3)+(2/5)= 1
解决方案：
(5x / 3) = 1 – (2 / 5)
Calculate LCM of 1 and 5 which is 5.
(5x / 3) = ((5 * 1) – 2) / 5
(5x / 3) = 3 / 5
Using cross multiplication we get,
25x = 9
x = 9 / 25
Verification:
Putting x = 9 / 25 in LHS we get,
= ((5 * (9 / 25)) / 3) + (2 / 5)
= (3 / 5) + (2/ 5)
= ((3 + 2) / 5)
= 1
LHS = RHS
Hence, verified.
问题3： x / 2 + x / 3 + x / 4 = 13
解决方案：
Calculate LCM of 2, 3 and 4 which is 12.
(6 * x + 4 * x + 3 * x) / 12 = 13
(13x) / 12 = 13
x = 12
Verification:
Putting x = 12 in LHS we get,
12 / 2 + 12 / 3 + 12 / 4
= (12 * 6 + 12 * 4 + 12 * 3) / 12
= (72 + 48 + 36) / 12
= 156 / 12
= 13
LHS = RHS
Hence, verified.
问题4： x / 2 + x / 8 = 1/8
解决方案：
Calculate LCM of 2 and 8 which is 8.
((4 * x + x) / 8 = 1 / 8
5x / 8 = 1 / 8
Using cross multiplication we get,
x = (1 * 8) / (8 * 5)
x = 1 / 5
Verification:
Putting x = 1 / 5 in LHS we get.
= ((1 / 5) / 2) + ((1 / 5) / 8)
= (1 / 10) + (1/ 40)
Calculate LCM of 10 and 40 which is 40.
= ((4 * 1) + 1) / 40
= 5 / 40
= 1 / 8
LHS = RHS
Hence, Verified
问题5： 2x / 3 – 3x / 8 = 7/12
解决方案：
Calculate LCM of 3 and 8 which is 24.
((2x * 8) – (3x * 3)) / 24 = 7 / 12
(16x – 9x) / 24 = 7 / 12
7x / 24 = 7 / 12
Using cross multiplication we get,
x = (7 * 24) / (12 * 7)
x = 2
Verification:
Putting x = 2 in LHS we get,
= (2 * 2) / 3 – (3 * 2) / 8
= 4 / 3 – 3 / 4
Calculate LCM of 3 and 4 which is 12.
= (4 * 4) – (3 * 3)/ 12
= (16 – 9) / 12
= 7 / 12
LHS = RHS
Hence, Verified.
问题6： (x + 2)(x + 3)+(x – 3)(x – 2)– 2x(x + 1)= 0
解决方案：
x (x + 3) + 2 (x + 3) + x (x – 2) -3 (x – 2) – 2x2 – 2x = 0
x2 + 3x + 2x + 6 + x2 – 2x – 3x + 6 – 2x2 – 2x = 0
x2 + x2 – 2x2 + 3x + 2x – 2x – 3x – 2x + 6 + 6 = 0
-2x + 12 = 0
12 = 2x
x = 6
Verification:
Putting x = 6 in LHS in we get,
= (6 + 2) (6 + 3) + (6 – 3) (6 – 2) – 2 * 6 (6 + 1)
= 8 * 9 + 3 * 4 – 12 * 7
= 72 + 12 – 84
= 0
LHS = RHS
Hence, Verified.
问题7： x / 2 – 4/5 + x / 5 + 3x / 10 = 1/5
解决方案：
x / 2 + x / 5 + 3x / 10 = 1 / 5 + 4 / 5
Calculate LCM of 2, 5, 10 which is 10.
(5x + 2x + 3x) / 10 = (1 + 4) / 5
10x / 10 = 5 / 5
x = 1
Verification:
Putting x = 1 in LHS we get,
= 1 / 2 – 4 / 5 + 1 / 5 + 3 / 10
= (1 * 5 – 4 * 2 + 1 * 2 + 3) / 10
= (5 – 8 + 2 + 3) / 10
= 2 / 10
= 1 / 5
LHS = RHS
Hence, Verified.
问题8： 7 / x + 35 = 1/10
解决方案：
7 / x = 1 / 10 – 35
Calculate LCM of 1 , 10 which is 10.
7 / x = (1 – (35 * 10)) / 10
7 / x = – 349 / 10
Using cross multiplication we get,
(7 * 10 / -349) = x
x = -70 / 349
Verification:
Putting x = -70 / 349 in LHS we get,
= 7 / (-70 / 349) + 35
= (7 * 349) / (- 70) + 35
= -349 / 10 + 35
= (-349 + 350) / 10
= 1/10
LHS = RHS
Hence, Verified.
问题9： (2x – 1)/ 3 –(6x – 2)/ 5 = 1/3
解决方案：
Calculate LCM of 3 and 5 which is 15.
(5 (2x – 1) – 3 (6x – 2)) / 15 = 1 / 3
(10x – 5 – 18x + 6) / 15 = 1 / 3
(-8x + 1) / 15 = 1 / 3
Using cross multiplication we get,
3 (-8x + 1) = 15
-24x + 3 = 15
-24x = 12
x = 12 / -24
x = – 1 /2
Verification:
Putting x = -1 / 2 in LHS we get,
(1* (-1 / 2) – 1) / 3 – (6 * (-1 / 2) – 2) / 5
(-1 – 1) / 3 – (-3 – 2) / 5
(-2 / 3) – (-5 / 5)
(-2 / 3) + 1
Calculate LCM of 1 and 3 which is 3.
(-2 + 1 * 3) / 3
1 / 3
LHS = RHS
Hence, Verified.
问题10：13(y – 4)– 3(y – 9)– 5(y + 4)= 0
解决方案：
13y – 52 – 3y + 27 – 5y – 20 = 0
13y – 3y -5y – 52 + 27 – 20 = 0
5y – 45 = 0
5y = 45
y = 9
Verification:
Putting y = 9 in LHS we get,
= 13 (9 – 4) – 3 (9 – 9) – 5 (9 + 4)
= 13 * 5 – 0 – 5 * 13
= 65 – 65
= 0
LHS = RHS
Hence, Verified.
问题11： (2/3)(x – 5)–(1/4)(x – 2)= 9/2
解决方案：
2x / 3 – 10 / 3 – x / 4 + 1 / 2 = 9 / 2
2x / 3 -x / 4 = 9 /2 + 10 / 3 – 1 / 2
Calculate LCM of 3 , 4 which is 12 and calculate LCM of 2, 3 which is 6.
(8x – 3x) / 12 = (9 * 3 + 10 * 2 – 1 * 3) / 6
5x / 12 = (27 + 20 – 3) / 6
5x / 12 = 44 / 6
x = (44 * 12) / (6 * 5)
x = 88 / 5
Verification:
Putting x = 88 / 5 in LHS we get,
(2 / 3) (88 / 5 – 5) – (1 / 4) (88 / 5 – 2)
(2 / 3) * ((88 – 25) / 5) – (1 / 4) * ((88 – 10) / 5)
(2 / 3) * (63 / 5) – (1 / 4) * (78 / 5)
42 / 5 – 39 / 10
Calculate LCM of 5 and 10 which is 10.
(42 * 2 – 39 * 1) / 10
(84 – 39) / 10
45 / 10
9 / 2
LHS = RHS
Hence, Verified.