有理表达式的和是多少：(3x + 2)/(x – 1) + (2x – 5)/(x – 1)？
几何是处理图形和尺寸的数学分支，算术是处理数字和运算的数学分支，同样，代数也是处理数字和变量的数学分支。具有恒定值的项称为数字并用数字表示。没有常数值的项称为变量，用字母和符号表示。
代数表达式
代数表达式是数字和变量与基本数学运算符的组合。通常，数学陈述是在数字和变量的帮助下以代数表达式的形式编写的。例如，从可以写为“x-9”的数字中减去 9。这里我们没有任何固定的数字值，所以我们假设它为 x。减号将语句分成两个术语。所以根据项数，代数表达式可以分为以下几类：
- 单项式：如果表达式中的项数为一个，则称为单项式。示例：8t、9y 等。
- 二项式：如果表达式中的项数为两个，则称为二项式。示例：8x – 8t、8t + 3 等
- 三项式：如果表达式中的项数为三，则称为三项式。示例：5a + 2b +3c、5q -9r +2t 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。
喜欢和不喜欢的条款
If the variable part of two or more terms of an expression is the same then these terms are known as the like terms and if the variable part of two or more terms of the expression is not the same then these terms are known as unlike terms. We do all the operations on the like terms.
For example: 5x3 – 3x2 + 2 – x + 2x2 – 9x
In the above expression, 3x3 and 2x2, -x and -9x are like terms.
有理表达式的和是多少：(3x + 2)/(x – 1) + (2x – 5)/(x – 1)？
解决方案：
Step to solve the problem:
Step 1: Figure out if the terms of the expression are in like fractions or not. If the denominator of the two or more fractions is the same then it is known as the like terms.
We can see in the given question denominator is (x – 1), so they are in like fractions.
Step 2: Apply the operation on the numerator part of the like part of the fraction.
= (3x + 2)/(x – 1) + (2x – 5)/(x – 1)
= (3x + 2 + 2x – 5)/(x – 1)
= (5x -3)/(x – 1)
Sum of the rational expressions (3x + 2)/(x – 1) + (2x – 5)/(x – 1) is (5x -3)/(x – 1).
类似问题
问题1：有理表达式的和是多少：(5x + 2)/(x + 4) + (2x – 5)/(x + 4)
解决方案：
In the given problem the denominator of both the term is the same, so they are like terms. Just simply do the operation on the numerator.
= (5x + 2 +2x – 5)/(x + 4)
Add the like terms.
= (7x – 3)/(x + 4)
问题2：有理表达式的和是多少：(5y – 9)/(3x + 2) + (2y +3)/(3x + 2)
解决方案：
In the given problem the denominator of both the term is the same, so they are like terms. Just simply do the operation on the numerator.
= (5y – 9 + 2y +3)/(3x + 2)
Add or subtract the like terms.
= (7y – 6)/(3x + 2)
问题3：有理表达式的和是多少：(y – 8)/(7x + 1) + (4y + 7)/(7x + 1)
解决方案：
In the given problem the denominator of both the term is the same, so they are like terms. Just simply do the operation on the numerator.
= (y – 8 + 4y + 7)/(7x + 1)
Now Add or subtract the like terms and we get,
= (5y – 1)/(7x + 1)