Explain how to add two rational expressions and how to subtract two rational expressions. How are the processes the same? How are they different?
do it the same way you work with normal fractions.
Find the common denominator and use that to adjust the numerators.
3/7 + 2/5 = (3*5 + 2*7)/(7*5)
To add or subtract two rational expressions, you follow similar processes, but with a slight difference. Let's start with the process of adding rational expressions:
1. Find a common denominator: Look for the least common multiple (LCM) of the denominators of the rational expressions involved. This will be the common denominator for the sum.
2. Express each rational expression with the common denominator: To do this, multiply the numerator and denominator of each fraction by the necessary factors to make the denominators equivalent to the common denominator.
3. Add or subtract the numerators: Once the rational expressions have the same denominator, you can add or subtract their numerators. Keep the common denominator.
4. Simplify if needed: Reduce the resulting fraction to its simplest form, if possible, by canceling out any common factors in the numerator and denominator.
Now let's move on to the process of subtracting rational expressions:
1. Find a common denominator: Just like in the addition process, you need to find the least common multiple (LCM) of the denominators involved. This will be the common denominator for the difference.
2. Express each rational expression with the common denominator: Multiply the numerator and denominator of each fraction by the necessary factors to make the denominators equivalent to the common denominator.
3. Subtract the numerators: Once the rational expressions have the same denominator, subtract the numerators while keeping the common denominator.
4. Simplify if necessary: As with addition, you may need to simplify the resulting fraction by canceling out any common factors in the numerator and denominator.
Now, let's compare the processes of adding and subtracting rational expressions:
Similarities:
1. Find a common denominator.
2. Express each rational expression with the common denominator.
3. Perform the operation on the numerators while keeping the common denominator.
4. Simplify the resulting fraction if possible.
Differences:
1. In addition, you add the numerators, while in subtraction, you subtract them.
2. In subtraction, it's important to subtract the second rational expression from the first, whereas in addition, you simply add the numerators.
Remember, practice is key to mastering these processes.