Rút gọn các biểu thức

To solve these equations, we will simplify each equation step by step and isolate the variable.

1) 16/(1/2)x + (1/6)x(x-2) = 3/4 - 2x

First, let's simplify the left side of the equation:
16/(1/2)x can be rewritten as 16 * 2/x = 32/x
(1/6)x(x-2) can be expanded as (1/6)x^2 - (1/3)x

Now, let's rewrite the equation:
32/x + (1/6)x^2 - (1/3)x = 3/4 - 2x

To get rid of the fractions, let's multiply the entire equation by the least common denominator (LCD), which is 12x:
12x * (32/x) + 12x * ((1/6)x^2 - (1/3)x) = 12x * (3/4 - 2x)

Simplifying further:
384 + 2x^3 - 4x^2 - 4x = 9x - 24x^2

Rearranging the terms:
2x^3 - 4x^2 - 4x + 9x - 24x^2 - 384 = 0

Combining like terms:
2x^3 - 28x^2 + 5x - 384 = 0

Unfortunately, this equation does not have a simple solution. You may need to use numerical methods or a graphing calculator to find an approximate solution.

2) 19/(5/12)x + 3 = 1/3 - (7/12)x

First, let's simplify the left side of the equation:
19/(5/12)x can be rewritten as 19 * 12/5x = 228/5x

Now, let's rewrite the equation:
228/5x + 3 = 1/3 - (7/12)x

To get rid of the fractions, let's multiply the entire equation by the least common denominator (LCD), which is 60x:
60x * (228/5x) + 60x * 3 = 60x * (1/3) - 60x * (7/12)x

Simplifying further:
456 + 180x = 20 - 35x^2

Rearranging the terms:
35x^2 + 180x + 456 - 20 = 0

Combining like terms:
35x^2 + 180x + 436 = 0

Unfortunately, this equation does not have a simple solution. You may need to use numerical methods or a graphing calculator to find an approximate solution.

3) 20/(1/2)x + 5/2 = 7/2x - 3/4

First, let's simplify the left side of the equation:
20/(1/2)x can be rewritten as 20 * 2/x = 40/x

Now, let's rewrite the equation:
40/x + 5/2 = 7/2x - 3/4

To get rid of the fractions, let's multiply the entire equation by the least common denominator (LCD), which is 4x:
4x * (40/x) + 4x * (5/2) = 4x * (7/2x) - 4x * (3/4)

Simplifying further:
160 + 10x = 14 - 3x

Rearranging the terms:
10x + 3x = 14 - 160

Combining like terms:
13x = -146

Dividing both sides by 13:
x = -146/13

Therefore, the solution to the equation is x = -146/13.