sums and differences of rational algebraic expression please answer the following 9ab/cd^2 - 7ab/cd^2 another 3/x-1 - 2/x-1 another is 4x/4x-y - 2x/4x-y another is 3x/2y - 3x-2y/3x+2y another is 8/3x - 3/4x + 4/12x another is x-3/3x+1 + x+5/3x+1
Take advantage of, or create, common denominators and add the numerators. These are the same kind of problems that Reiny has already answered for you.
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To find the sums and differences of rational algebraic expressions, we need to combine like terms.
Let's start with the first expression: 9ab/cd^2 - 7ab/cd^2.
1. The first step is to check if the denominators are the same. In this case, both expressions have the same denominator (cd^2).
2. Next, we can subtract the numerators while keeping the common denominator. So we have (9ab - 7ab) / cd^2.
3. Simplify the numerator: 9ab - 7ab = 2ab.
4. Putting it all together, the answer is 2ab/cd^2.
Now let's move on to the second expression: 3/(x-1) - 2/(x-1).
1. As with the first expression, we see that the denominators are the same (x-1).
2. Subtract the numerators while keeping the common denominator: (3 - 2) / (x-1).
3. Simplify the numerator: 3 - 2 = 1.
4. The final result is 1/(x-1).
Now let's solve the next expressions using the same steps:
- For 4x/4x-y - 2x/4x-y: The denominators are the same (4x-y), so subtract the numerators: (4x - 2x) / (4x-y) = 2x/(4x-y).
- For 3x/2y - (3x-2y)/(3x+2y): We need to find the common denominator, which is (2y)*(3x+2y). Multiply each term accordingly: (3x*(3x+2y))/(2y*(3x+2y)) - (2*(3x-2y))/(2y*(3x+2y)). Now we can simplify the expression: (9x^2 + 6xy - 6x + 4y)/(6xy + 4y^2).
- For 8/3x - 3/4x + 4/12x: The denominators are different, so we need to find the least common denominator (LCD), which is 12x. Adjust the numerators accordingly: (8*4/(3x*4)) - (3*3/(4x*3)) + 4/12x. Now we can simplify the expression: (32/12x) - (9/12x) + 4/12x = (23/12x).
- For (x-3)/(3x+1) + (x+5)/(3x+1): Here, we already have the same denominator (3x+1). Add the numerators: (x-3 + x+5) / (3x+1) = (2x+2)/(3x+1).
Remember, when working with rational algebraic expressions, always look for like terms (same denominator) and perform the necessary operations.