简化 (10x 2 )/5x
代数是我们研究数字和变量的数学分支。数字和变量通过基本算术运算运算符连接在一起。代数的主要用途是寻找未知数。我们还使用代数推导公式。例如，如果我们必须找到矩形的周长，则需要矩形的长度和宽度。假设长度为“l”，宽度为“b”，则矩形的周长为 2×(l+b)。对于不同的长度和宽度值，可以使用上式计算矩形的周长。
Algebraic Expression
An algebraic expression is the combination of numerals, variables, and arithmetic operators. An algebraic expression is the mathematical form of a statement.
For example: 9 is taken away from three times a number can be written as ‘3x-9’.
Here we suppose the unknowns as x because don’t know the exact value of that number. The term which has fix value is known as numerals and the term which do not have fix value is known as a variable. We generally represent variables by letters of the alphabet.
在上述表达式中，负号将表达式分为两项。根据项数，代数表达式分为以下几部分。
- 单项式：如果代数表达式的项数为一个，则称为单项式。示例：8x、6y 等
- 二项式：如果代数表达式中的项数为两个，则称为二项式表达式。示例：5x+8、9y+6z 等
- 三项式：如果代数表达式中的项数为三，则称为三项式。示例：9a+3b-6c、8m+3n-6p 等
- 多项式：如果代数表达式中的项数为一项或多项，则称为多项式。
Division of the algebraic expression:
Write the numerator and denominator of the algebraic expression in the factors form. Then find out the like terms in numerator and denominator and cancel them. The remaining term will be the answer to the given algebraic expression.
解决问题的步骤：
第 1 步：将分子和分母写入因式分解形式。
步骤2：找出分子和分母的相似项并取消它们。
第 3 步：以最简单的形式写出剩余的项。那将是答案。
简化 (10x 2 )/5x。
解决方案：
Factorise the numerator and denominator.
The numerator can be written as = 2 × 5 × x × x
The denominator can be written as = 5 × x
Put these values in fraction form.
= (2 × 5 × x × x)/(5 × x)
Cancel out the common term of numerator and denominator.
= 2 × x
= 2x
So the simplification of (10x²)/5x is 2x.
类似问题
问题 1：简化 36x²/27x。
解决方案：
Factorise the numerator and denominator.
The numerator can be written as = 2 × 2 × 3 × 3 × x × x
The denominator can be written as = 3 × 3 × 3 × x
Put these values in fraction form.
= (2×2×3×3×x×x)/(3×3×3×x)
Cancel out the common term of numerator and denominator.
= (2 × 2 × x)/3
= 4x/3
So the simplification of 36x²/27x is 4x/3.
问题 2：简化 9y³/3y²。
解决方案：
Factorise the numerator and denominator.
The numerator can be written as = 3×3×y×y×y
The denominator can be written as = 3×y×y
Put these values in fraction form.
= (3×3×y×y×y)/(3×y×y)
Cancel out the common term of numerator and denominator.
= 3×y
= 3y
So the simplification of 9y³/3y² is 3y.