化简 (2/(3k)) + (k/(k + 1)) 除以 (k/(k + 1)) – (3/k)

代数是数学的一个分支，我们在其中研究寻找未知数的值。它由数字、变量和基本算术运算运算符组成。具有常数值的项称为数字，用数字表示，没有常数值的项称为变量，用字母或符号表示。代数基本上用于借助变量或符号来形式化数学中的不同公式。

代数表达式

代数表达式是数字、变量和运算符的系统表示。它基本上是将数学语句表示为数学表达式。

例如，“从 21 中减去一个数的三次”可以写为“21 – 3x”。这里我们不知道数字，所以我们用 x 表示它。负号将表达式分成两项。因此，根据术语的数量，表达式可以分为以下类型。

• 单项式：如果表达式中的项数为一个，则称为单项式。例如9t、6y等
• 二项式：如果表达式中的项数为两个，则称为二项式表达式。示例：8x-9y、8t-6u 等。
• 三项式：如果表达式中的项数为三，则称为三项式。示例：8a+3b+5c、8e-6g-6s 等。
• 多项式：如果表达式中的项数为一个或多个，则称为多项式。

Like terms and unlike terms

If the variable terms of an expression are the same then it is known as the like terms of an algebraic expression and if variable terms are not the same then it is known as unlike terms.

For example: 9x² – 6y +3x -5x² +4y – 9

In the above expression, 9x² and 5x² have the same variable, 6y and 4y have the same variable. So these terms are like terms.

化简 (2/(3k)) + (k/(k+ 1)) 除以 (k/(k + 1)) – (3/k)

解决方案：

Step to solve the problem:

Step 1: Write the given mathematical statement in expression with the help of numerals, variables, and operators accordingly.

= {(2/(3k) + (k/(k+1))} ÷ {(k/(k + 1)) – (3/k)}

Step 2: Simplify the bracket part first. If the denominator of the fraction is not the same then do the cross multiplication and simply.

= [{(2×(k+1) + (k×3k)}/(3k)×(k+1)] ÷ [{(k×k) – 3×(k+1)}/k×(k+1)]

= {(2k+2+3k²)/3k×(k+1)} ÷ {(k²-3k-3)/k×(k+1)}

Step 3: If a fraction is divided by another fraction then it can be written as:

(a/b)÷(c/d)=(a×d)/(b×c)

= {(2k+2+3k²)×(k×(k+1))/3k×(k+1)×((k²-3k-3)}

Step 4: Cancel to the common factor of the numerator and denominator.

= (3k²+2k+2)/(k²-3k-3)

This expression can not further simplified. So the simplification of  (2/(3k)) + (k/(k+ 1)) divided by (k/(k + 1)) – (3/k) is (3k²+2k+2)/(k²-3k-3).

类似问题

问题 1：化简 (2/(5x)) + (x/(x+ 3)) 除以 (x/(x + 3)) – (6/x)。

解决方案：

Write the given mathematical statement in expression with the help of numerals, variables, and operators accordingly.

= {(2/(5x)) + (x/(x+ 3))} ÷ {(x/(x + 3)) – (6/x)}

Simplify the bracket part first. If the denominator of the fraction is not the same then do the cross multiplication and simply.

= {(2×(x+3)+5x×x)/(5x×(x+3)} ÷ {(x×x -6×(x+3))/(x×(x+3))}

= {(2x+6+5x²)/(5x×(x+3))} ÷ {(x²-6x-18)/(x×(x+3))}

If a fraction is divided by another fraction then it can be written as: (a/b)÷(c/d)=(a×d)/(b×c)

= {(2x+6+5x²)×(x×(x+3))}/{(5x×(x+3)×(x²-6x-18)}

Cancel to the common factor of the numerator and denominator.

= (5x²+2x+6)/(5×(x²-6x-18))

= (5x²+2x+6)/(5x²-30x-90)

So the simplification of (2/(5x)) + (x/(x+ 3)) divided by (x/(x + 3)) – (6/x) is (5x²+2x+6)/(5x²-30x-90).

问题2：化简3a/(a+2)-1除以(a×(a+6))/(a+2)+2。

解决方案：

Write the given mathematical statement in expression with the help of numerals, variables, and operators accordingly.

= {3a/(a+2)-1} ÷ {(a×(a+6))/(a+2)+2}

Simplify the bracket part first. If the denominator of the fraction is not the same then do the cross multiplication and simply.

= {(3a-a-2)/(a+2)} ÷ {(a²+6a+2a+4)/(a+2)

= {(2a-2)/(a+2)} ÷ {(a²+8a+4)/(a+2)}

= {2(a-1)/(a+2)} ÷ {(a²+8a+4)/(a+2)}

If a fraction is divided by another fraction then it can be written as: (a/b)÷(c/d) = (a×d)/(b×c)

= {2×(a-1)×(a+2)}/{(a+2)×(a²+8a+4)}

Cancel to the common factor of the numerator and denominator.

= 2(a-1)/(a²+8a+4)

So the simplification of 3a/(a+2)-1 divided by (a×(a+6))/(a+2)+2 is 2(a-1)/(a²+8a+4)