x+4/2 - x-1/5 + 2x+5/10 another is 3b/7a - a/2b + 3a^2-2b^2/14ab another is 2x-y/3x+y + 5x/2y this is an rational algebraic expression my topic is all about sums and differences of rational algebraic expression please answer this please HELP ME!
To simplify rational algebraic expressions, we need to follow certain rules and steps. Let's go through each of the given expressions and simplify them:
Expression 1: x + 4/2 - x - 1/5 + 2x + 5/10
1. Combine the like terms. Like terms have the same variables raised to the same powers.
(x - x) + (2x) = 2x
4/2 - 1/5 + 5/10 = 2/1 - 1/5 + 1/2
2. Convert all fractions to have the same denominator.
In this case, the lowest common denominator (LCD) is 10.
2/1 - 1/5 + 1/2 = (2*5)/(1*5) - 1/5 + 5/10
10/5 - 1/5 + 5/10
3. Combine the fractions.
10/5 - 1/5 + 5/10 = 2 - 1/5 + 1/2
2 - 1/5 + 5/10
4. Convert the mixed numbers to improper fractions.
2 = 2/1
2/1 - 1/5 + 5/10 = 2/1 - 1/5 + 5/10
2/1 - 1/5 + (5*1)/(10*1)
2/1 - 1/5 + 5/10
5. Convert all fractions to have the same denominator (LCD).
In this case, the lowest common denominator (LCD) is 10.
2/1 - 1/5 + 5/10 = (2*10)/(1*10) - (1*2)/(5*2) + 5/10
20/10 - 2/10 + 5/10
6. Combine the fractions.
20/10 - 2/10 + 5/10 = 20 - 2 + 5/10
18 + 5/10
Thus, the simplified expression is: 18 + 5/10.
Expression 2: 3b/7a - a/2b + 3a^2 - 2b^2/14ab
1. Combine the like terms. There are no like terms in this expression.
Thus, the expression cannot be further simplified.
Expression 3: 2x - y/3x + y + 5x/2y
1. Combine the like terms.
2x + 5x = 7x
-y + y = 0y (y - y = 0)
2. Rewrite the expression using the combined like terms.
7x - y/3x + 0 + 2/2y
3. Simplify the expression.
Since 0 + 2/2y equals 2/2y, we can rewrite the expression as:
7x - y/3x + 2/2y
Thus, the simplified expression is: 7x - y/3x + 2/2y.