When you multiply rational expressions they must have a common denominator. (1 point)
1. True
2. False
2. False
1. True
The correct answer is 1. True.
When you multiply rational expressions, you must indeed have a common denominator.
To understand why this is necessary, let's first review what a rational expression is. A rational expression is the ratio of two polynomial expressions, where the numerator and denominator can both be polynomials.
When multiplying two rational expressions, you need to multiply both the numerators and the denominators. The multiplication of the numerators is straightforward – you simply multiply the polynomials.
However, when it comes to the denominators, you need to have a common denominator before you can multiply. When you multiply two fractions with different denominators, you cannot directly multiply the denominators together. Instead, you need to find a common denominator.
Finding a common denominator involves identifying the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators divide evenly into. Once you find the LCM, you can then convert each fraction to an equivalent fraction with the common denominator before multiplying.
By having a common denominator, you ensure that the fractions can be multiplied together correctly, and the resulting expression is in its simplest form.
Therefore, to multiply rational expressions correctly, you must have a common denominator, making the statement "When you multiply rational expressions, they must have a common denominator" true.