find the lcd of this rational algebraic expression 4/x+2,2/2-x,3/4-x^2 another rational algebraic expression you will also find the lcd 5/y+5,3y/2y+10,2/y+10
To find the least common denominator (LCD) of rational algebraic expressions, follow these steps:
Step 1: Factor all denominators
Step 2: Identify the common factors
Step 3: Multiply the common factors to find the LCD
Let's find the LCD for the first set of rational algebraic expressions:
1. Find the LCD for 4/x + 2, 2/2 - x, and 3/4 - x^2:
Step 1: Factor all denominators:
- The denominator of the first expression is x.
- The denominator of the second expression is 2 - x. (Note: We've switched the order of the terms to match the typical format of an algebraic expression.)
- The denominator of the third expression is 4 - x^2, which is the difference of two squares and can be further factored as (2 + x)(2 - x).
Step 2: Identify the common factors:
- The common factors among x, 2 - x, and (2 + x)(2 - x) are (2 + x) and (2 - x).
Step 3: Multiply the common factors to find the LCD:
- The LCD is (2 + x)(2 - x) = (2^2 - x^2) = 4 - x^2.
Thus, the LCD of 4/x + 2, 2/2 - x, and 3/4 - x^2 is 4 - x^2.
Now, let's find the LCD for the second set of rational algebraic expressions:
2. Find the LCD for 5/y + 5, 3y/2y + 10, and 2/y + 10:
Step 1: Factor all denominators:
- The denominator of the first expression is y.
- The denominator of the second expression is 2y + 10, which can be further factored as 2(y + 5).
- The denominator of the third expression is y + 10.
Step 2: Identify the common factors:
- The common factors among y, 2(y + 5), and y + 10 are y and (y + 5).
Step 3: Multiply the common factors to find the LCD:
- The LCD is y(y + 5).
Thus, the LCD of 5/y + 5, 3y/2y + 10, and 2/y + 10 is y(y + 5).