将方程式简化为简单形式八级数学

简化方程是一种求解复杂方程并将方程写为简单形式的方法。并非所有的方程都是线性方程的形式(线性方程是一阶方程。)，但是可以通过对它们执行一些数学运算(例如交叉乘法)，将它们变成线性方程的形式来求解。在将这些非线性方程式简化为线性形式后，可以求解它们，并且可以轻松地计算变量的值。

将方程式简化为简单形式的步骤

1.如果给定方程为非线性形式，则无法直接求解。因此，首先，我们将需要使用交叉乘法技术来简化给定的方程。

2.对等式的两边进行叉乘运算，即，一侧的分母与另一侧的分子相乘。

3.使用分配法打开括号。

4.将所有变量放在等式的一侧(LHS)，将常数放在等式的另一侧(RHS)

5.将其余方程作为一个变量求解为线性方程。

 x – y / y = y – x / x

Step 1 : Doing cross multiplication we get: 

 x (x – y) = y (y – x)

 x² – xy = y² – xy

Step 2 : Bring all the x variables on one side i.e. LHS and all the y variable on the other side i.e. RHS

 x² – xy + xy = y² 

 x² = y²

Step 3 : Taking square root on both the side we get,

   x = y

现在让我们举一些例子来理解以更简单的形式简化方程式的方法。

示例1. x – 1 / x + 2 = 1/6

解决方案 ：

Step 1 : As the equation is in non-linear form, so this cannot be directly solved. Therefore, first we will need to simplify the given equation by using the Cross Multiplication technique. 

  x – 1 / x + 2 = 1 / 6

Cross Multiplication technique : The denominator on both sides are multiplied to the numerator on the other side.

Step 2 :  After cross multiplication, the equation can be written as: 

 6 (x – 1) = 1 (x + 2)            

Step 3 : Now open the parentheses by using distributive law

 6x – 6 = x + 2

Step 4 : Bring all the variables on one side i.e. LHS and all the constants on the other side i.e. RHS

 6x – x = 2 + 6

 5x = 8

Step 5: Dividing both the sides by 5

 x = 8/5

示例2. 2x – 3 / 2x + 2 = 1/6

解决方案 ：

 = 2x – 3 / 2x + 2 = 1 / 6 [simplifying the given equation by using the Cross Multiplication technique]

= 6 (2x – 3) = 1 (2x + 2)            

=12x – 18  = 2x + 2 [using distributive law]

=12x – 2x = 2 + 18

=10x = 20

= x = 2 [Dividing both the sides by 10]

示例3. x / 2 – 1/5 = x / 3 + 1/4

解决方案 ：

As the given equation is in the complex form, we have to reduce it into a simpler form.

= Take the L.C.M. of the denominators 2, 5, 3 and 4 which is 60.

= x * 60 / 2 – 1  60 / 5 = x * 60 /3 + 1 * 60 /4 [Multiply both the sides by 60]

= 30x −12 = 20x + 15

= 30x − 20x = 15 + 12

=10x = 27

= x = 2.7 [Dividing both the sides by 10]

例子4. x – 1 = x / 3 + 3/4

解决方案：

= Take the L.C.M. of the denominators 3 and 4 which is 12.

= x * 12 – 1 * 12 = x * 12 /3 + 3 * 12 /4 [Multiply both the sides by 12]

= 12x −12 = 4x + 9

= 12x − 4x = 9 + 12

 = 8x = 31

= x = 31/8 [Dividing both the sides by 8]