IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.
Sagot :
First, some general rules to remember:
Rational expressions (fractions) can only be added or subtracted if they have a common denominator.
The numerator and denominator of a fraction may be multiplied by the same quantity. This will result in a fraction that is equivalent to the original fraction.
For a fractional answer to be in final form, the fraction must be reduced to lowest terms.
Adding or subtracting rational expressions is a four-step process:
Write all fractions as equivalent fractions with a common denominator.
Combine the fractions as a single fraction that has the common denominator.
Simplify the expression in the top of the fraction.
Reduce the fraction to lowest terms.
To see this process, we'll look at some examples.
Example 1
Step 1: To find a common denominator, start by factoring the denominators of both fractions.
The least common denominator of these two fractions is 2(x+6)(x-6).
Looking at the first fraction, we can see that the factor missing from its denominator is (x-6). In the next step, we'll multiply the top and bottom of the first fraction by (x-6).
Looking at the second fraction, we can see that the factor missing from its denominator is 2. In the next step, we'll multiply the top and bottom of the second fraction by 2.
Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:
Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.
Step 4: Now we'll reduce the fraction to lowest terms
Example 2
Step 1: To find a common denominator, start by factoring the denominators of both fractions.
The least common denominator of these two fractions is (x+4)(x+1)(x+3).
Looking at the first fraction, we can see that the factor missing from its denominator is (x+3). In the next step, we'll multiply the top and bottom of the first fraction by (x+3).
Looking at the first fraction, we can see that the factor missing from its denominator is (x+4). In the next step, we'll multiply the top and bottom of the first fraction by (x+4).
Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:
Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.
Step 4: Now we'll reduce the fraction to lowest terms
Rational expressions (fractions) can only be added or subtracted if they have a common denominator.
The numerator and denominator of a fraction may be multiplied by the same quantity. This will result in a fraction that is equivalent to the original fraction.
For a fractional answer to be in final form, the fraction must be reduced to lowest terms.
Adding or subtracting rational expressions is a four-step process:
Write all fractions as equivalent fractions with a common denominator.
Combine the fractions as a single fraction that has the common denominator.
Simplify the expression in the top of the fraction.
Reduce the fraction to lowest terms.
To see this process, we'll look at some examples.
Example 1
Step 1: To find a common denominator, start by factoring the denominators of both fractions.
The least common denominator of these two fractions is 2(x+6)(x-6).
Looking at the first fraction, we can see that the factor missing from its denominator is (x-6). In the next step, we'll multiply the top and bottom of the first fraction by (x-6).
Looking at the second fraction, we can see that the factor missing from its denominator is 2. In the next step, we'll multiply the top and bottom of the second fraction by 2.
Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:
Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.
Step 4: Now we'll reduce the fraction to lowest terms
Example 2
Step 1: To find a common denominator, start by factoring the denominators of both fractions.
The least common denominator of these two fractions is (x+4)(x+1)(x+3).
Looking at the first fraction, we can see that the factor missing from its denominator is (x+3). In the next step, we'll multiply the top and bottom of the first fraction by (x+3).
Looking at the first fraction, we can see that the factor missing from its denominator is (x+4). In the next step, we'll multiply the top and bottom of the first fraction by (x+4).
Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:
Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.
Step 4: Now we'll reduce the fraction to lowest terms
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.
