Multiplication and Division of Algebraic Fractions
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Multiplication and Division Operations in Algebraic Fractions
When we want to multiply or divide algebraic fractions, we will use the same tools that we use for the multiplication or division of common fractions with some small differences.
Steps to carry out for the multiplication of algebraic fractions 1:
Let's try to extract the common factor. This can be the variable or any free number.
If this is not enough, we will factorize with short multiplication formulas or with trinomials.
Let's find the solution set.
How is the solution set found? We will make all the denominators we have equal to 0 and find the solution. The solution set will be X: different from what causes our denominator to equal zero.
Let's simplify the fractions with determination.
Multiply numerator by numerator and denominator by denominator as in any fraction.
Steps to carry out for the division of algebraic fractions2:
We will convert the division exercise into a multiplication one, as we do with common fractions. How will we do it correctly? We will leave the first fraction as it is, change the division sign to a multiplication sign, and invert the fraction that appears after the sign. That is, numerator instead of denominator and denominator instead of numerator.
We will act according to the rules of multiplication of algebraic fractions:
Let's try to extract the common factor. This can be the unknown or any free number.
If this is not enough, we will factorize using short multiplication formulas and with trinomials.
Let's find the solution set.
How is the solution set found? We will make all the denominators we have equal to 0 and find the solution. The solution set will be X: different from what causes our denominator to equal zero.
Let's simplify the fractions with determination.
Multiply numerator by numerator and denominator by denominator as in any fraction.
Let's look at an example of multiplying algebraic fractions
x+3x+2โรx2โ43x+9โ=
Let's try to factorize by extracting the common factor and with the shortcut multiplication formulas, and we will obtain: x+3x+2โร(xโ2)(x+23(x+3)โ=
Let's find the solution set:
x๎ =โ3,2,โ2
Let's reduce the fractions and we will obtain:
1ร(xโ2)3โ= Multiply and it will give us: xโ23โ
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Question 1
Select the field of application of the following fraction:
Let's convert the division exercise into a multiplication one:
x2โ3x+2x2โ8x+15โรx2โ9xโ1โ= Now, let's factor and we will get: (xโ2)(xโ1)(xโ5)(xโ3)โร(xโ3)(x+3)xโ1โ= Let's find the solution set: x๎ =2,1,3,โ3
Let's simplify, we will get:
xโ2xโ5โรx+31โ
Let's multiply and it will give us: (xโ2)(x+3)xโ5โ
If you are interested in this article, you might also be interested in the following articles:
The uses of factorization
Factorization according to short multiplication formulas
Factorization through the extraction of the common factor outside the parentheses
Factorization of trinomials
Factorization of algebraic fractions
Addition and subtraction of algebraic fractions
Simplification of algebraic fractions
Solving equations through factorization
In theTutorelablog, you will find a variety of articles about mathematics.
Examples and exercises with solutions for multiplication and division of algebraic fractions
examples.example_title
Determine if the simplification described here is true or false:
6โ 36โ 3โ=1
examples.explanation_title
We simplify the expression on the left side of the approximate equality:
๎ 6โ ๎ 3๎ 6โ ๎ 3โ=?1โ1=!1therefore, the described reduction is correct.
Therefore, the correct answer is option A.
examples.solution_title
True
examples.example_title
Determine if the simplification described here is true or false:
8โ 35โ 8โ=35โ
examples.explanation_title
Let's consider the fraction and break it down into two multiplication exercises:
88โร35โ
We simplify:
1ร35โ=35โ
examples.solution_title
True
examples.example_title
Determine if the simplification described here is true or false:
44โ 8โ=81โ
examples.explanation_title
We will divide the fraction exercise into two multiplication exercises:
44โร18โ=
We simplify:
1ร18โ=8
Therefore, the described simplification is false.
examples.solution_title
False
examples.example_title
Determine if the simplification described here is true or false:
7โ 33โ 7โ=0
examples.explanation_title
We will divide the fraction exercise into two different multiplication exercises, As this is a multiplication exercise, you can use the substitution property:
77โร33โ=1ร1=1
Therefore, the simplification described is false.
examples.solution_title
False
examples.example_title
Determine if the simplification described here is true or false:
7โ 87โ=8
examples.explanation_title
Let's consider the fraction and break it down into two multiplication exercises:
77โร81โ
We simplify:
1ร81โ=81โ
Therefore, the described simplification is false.
examples.solution_title
False
Do you know what the answer is?
Question 1
Determine if the simplification described here is true or false: