求解 (7m + 14)/(5m + 10)

代数表达式由变量和常数以及诸如加法、减法等代数运算组成。这些表达式由项组成。代数表达式是对任何变量进行加减乘除等运算时的方程。

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as an algebraic expression (or) a variable expression.

e.g.: 2x + 4y – 7, 3x – 10, etc.

一些重要的代数公式

有一些代数表达式的术语被广泛使用，

(a + b)² = a² + 2ab + b²

(a – b)² = a² – 2ab + b²

(a + b)(a – b) = a² – b²

(x + a)(x + b) = x² + x(a + b) + ab

(a + b)³ = a³ + b³ + 3ab(a + b)

(a – b)³ = a³ – b³ – 3ab(a – b)

a³ – b³ = (a – b)(a² + ab + b²)

a³ + b³ = (a + b)(a² – ab + b²)

求解 (7m + 14)/(5m + 10)

解决方案：

A fraction in which the numerator and denominator are polynomials is termed as a Rational expression. In Rational expression, the denominator can never have zero value.

In other words, An algebraic expression which can be written as a ratio of two polynomial expressions is defined as a Rational expression.  

To simplify the rational expression, Eliminate the common factors in both the numerator and denominator. 

Here Given: {7m + 14}/{5m +10} 

First find the common factor from numerator and denominator

= {7m + 14}/{5m +10} 

= {7(m + 2)}  / {5(m + 2)}

By simplifying (m + 2) is common 

= 7/5 is the lowest term 

示例问题

问题 1：用最低的形式写出有理式。 {3m + 9}/{5m +15}？

解决方案：

A fraction in which the numerator and denominator are polynomials is termed as a Rational expression. In Rational expression, the denominator can never have zero value.

In other words, an algebraic expression which can be written as a ratio of two polynomial expressions is defined as a Rational expression.  

To simplify the rational expression, Eliminate the common factors in both the numerator and denominator.

here Given : {3m + 9}/{5m +15}

First find the common factor from numerator and denominator

  = {3m + 9}/{5m +15}

  = {3(m + 3)} / {5(m + 3)}

By simplifying (m+3) is common

  = 3/5 is the lowest term 

问题 2：用最低的形式写出有理式。 {4x ² + 8x + 12}/{6x ² + 12x +18}？

解决方案：

A fraction in which the numerator and denominator are polynomials is termed as a Rational expression. In Rational expression, the denominator can never have zero value.

In other words, an algebraic expression which can be written as a ratio of two polynomial expressions is defined as a Rational expression.  

To simplify the rational expression, Eliminate the common factors in both the numerator and denominator.

here Given: {4x² + 8x + 12}/{6x² + 12x +18}

First find the common factor from numerator and denominator

 = {4x² + 8x + 12}/{6x² + 12x +18}

 = {4(x² + 2x + 3)}  / {6(x² + 2 + 3)}

By simplifying (x² + 2x + 3) is common

 =  4/6

 = 2/3 is the lowest term 

问题 3：简化：4 – 2(x – 2)

解决方案：

Here we have

4 – 2(x – 2)

= 4 – 2x + 4

= 8 – 2x

= -2x + 8

= -2(x – 4) 

问题 4：用最低的形式写出有理式。 {4m + 16}/{6m + 24}？

解决方案：

A fraction in which the numerator and denominator are polynomials is termed as a Rational expression. In Rational expression, the denominator can never have zero value.

In other words, an algebraic expression which can be written as a ratio of two polynomial expressions is defined as a Rational expression.  

To simplify the rational expression, Eliminate the common factors in both the numerator and denominator.

Given: {4m + 16}/{6m + 24}

First find the common factor from numerator and denominator

 =  {4m + 16}/{6m + 24}

 = {4(m + 4)} / {6(m + 4)}

By simplifying (m+4) is common

 = 4/6

 = 2/3 is the lowest term 

问题 5：简化：5 – 2(x – 2) + 3x

解决方案：

Here we have 5 – 2(x – 2) + 3x

= 5 – 2x + 4 + 3x

= 9 + x

= x + 9

问题 6：化简 3x + 3(x – 1) = 33

解决方案：

Given: 3x + 3(x – 1) = 33

3x + 3x – 3 = 33

6x – 3 = 33

6x = 33 + 3

6x = 36

x = 36/6

x = 6

问题 7：用最低的形式写出有理式。 {10x + 50}/{20x + 100}？

解决方案：

A fraction in which the numerator and denominator are polynomials is termed as a Rational expression. In Rational expression, the denominator can never have zero value.

In other words, an algebraic expression which can be written as a ratio of two polynomial expressions is defined as a Rational expression.  

To simplify the rational expression, Eliminate the common factors in both the numerator and denominator.

here Given: {10x + 50}/{20x + 100}

First find the common factor from numerator and denominator

= {10x + 50}/{20x + 100}

= {10(x + 5)}  / {20(x + 5)}

By simplifying (x +5) is common

= 10/20

= 1/2 is the lowest term