when adding or subtracting rational exprssions, why do you need an LCD
The rules for numerators and denominators are different. When adding or subtracting fractions, or fractional algebraic terms, the denominators must be the same. Then, you can add or subtract the numerators while keeping the common denominator.
The reason should be obvious when you think about it. When you have a series of numbers with the same denominator x, the ratio of their sizes is the ratio of the numerators.
Thus a/x + b/x = (a+b)*(1/x) = (a+b)/x
You cannot write an analogous valid expression to justify adding denominators with a common numerator. instead, you have
x/a + x/b = x(1/a + 1/b), = x(b+a)/ab
3 4/9 x 1 4/5 show work please
When adding or subtracting rational expressions, you need to find a common denominator, which is also known as the least common denominator (LCD). The LCD is required in this process to ensure that both expressions have the same denominator, allowing you to combine them.
The process of adding or subtracting rational expressions involves these steps:
1. Factorize the denominators of the rational expressions if needed.
2. Identify the common factors and non-common factors among the denominators.
3. Determine the LCD by taking the product of the non-common factors and the common factors raised to their highest power.
4. Rewrite each rational expression, making the denominators equal to the LCD.
5. Perform the addition or subtraction operation on the numerators of the rational expressions, while keeping the common denominator.
6. Simplify the resulting expression, if possible.
By finding the LCD, you ensure that both rational expressions have the same denominator, which is crucial for performing addition or subtraction. This step enables you to combine the numerators correctly and create an equivalent expression.