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Solve (7m + 14)/(5m + 10)

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  • Last Updated : 11 Mar, 2022

Algebraic Expression is made up of variables and constants along with algebraic operations such as addition, subtraction, etc.. these Expressions are made up of terms. Algebraic expressions are the equations when the operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.

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.

Some Important Algebraic Formulas

There are some terms of algebraic expression which are widely used,

(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)

Solve (7m + 14)/(5m + 10)

Solution:

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 

Sample Questions

Question 1: Write the rational expression in lowest terms. {3m + 9}/{5m +15}?

Solution: 

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 

Question 2: Write the rational expression in lowest terms. {4x2 + 8x + 12}/{6x2 + 12x +18}?

Solution: 

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 

Question 3: Simplify: 4 – 2(x – 2)

Solution:

Here we have

4 – 2(x – 2)

= 4 – 2x + 4

= 8 – 2x

= -2x + 8

= -2(x – 4) 

Question 4: Write the rational expression in lowest terms. {4m + 16}/{6m + 24}?

Solution: 

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 

Question 5: Simplify: 5 – 2(x – 2) + 3x 

Solution: 

Here we have 5 – 2(x – 2) + 3x

= 5 – 2x + 4 + 3x

= 9 + x

= x + 9

Question 6: Simplify 3x + 3(x – 1) = 33

Solution: 

Given: 3x + 3(x – 1) = 33

3x + 3x – 3 = 33

6x – 3 = 33

6x = 33 + 3

6x = 36

x = 36/6

x = 6

Question 7: Write the rational expression in lowest terms. {10x + 50}/{20x + 100}?

Solution: 

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 

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