can you answer this please about sums and differences of a rational algebraic expression this is the problem 5/x-7 - x-1/x-7 - 2+x/x-7 another is x+1/2 - x-2/3 + 2x-1/9 another is 2x+3/3 - 3x-1/2 + x-4/12
did you mean
5/(x-7) - (x-1)/(x-7) - (2+x)/(x-7)
since you already have a common denominator, just add/subtract the numerators
= (5 - x + 1 - 2 - x)/(x-7)
= (4-2x)/(x-7)
for the second, your common denominator would be the LCM of 2,3, and 9 which would be 18
(x+1)/2 - (x-2)/3 + (2x-1)/9
= [9(x+1) - 6(x-2) + 2x-1 ] /9
= .....
third one is just as easy, the LCD is 12
obviously I have a typo in the second question, should say ...
(x+1)/2 - (x-2)/3 + (2x-1)/18
= [9(x+1) - 6(x-2) + 2x-1 ] /18
= .....
Sure! I can help you with those problems. Let's start by simplifying each expression step-by-step.
Problem 1: 5/(x - 7) - (x - 1)/(x - 7) - (2 + x)/(x - 7)
To simplify this expression, we need to find a common denominator for all the fractions. In this case, the common denominator is (x - 7).
Rewriting the expression with the common denominator:
(5 - (x - 1) - (2 + x))/(x - 7)
Now, let's simplify the numerator:
(5 - x + 1 - 2 - x)/(x - 7)
Combining like terms in the numerator:
(-2x + 4)/(x - 7)
Thus, the simplified expression is (-2x + 4)/(x - 7).
Problem 2: (x + 1)/2 - (x - 2)/3 + (2x - 1)/9
Again, we need to find a common denominator for all the fractions. The common denominator here is 18 (which is the least common multiple of 2, 3, and 9).
Rewriting the expression with the common denominator:
((x + 1)(9/9) - (x - 2)(6/6) + (2x - 1)(2/2))/18
Simplifying further:
(9(x + 1) - 6(x - 2) + 2(2x - 1))/18
Expanding and simplifying the numerator:
(9x + 9 - 6x + 12 + 4x - 2)/18
Combining like terms:
(7x + 19)/18
Hence, the simplified expression is (7x + 19)/18.
Problem 3: (2x + 3)/3 - (3x - 1)/2 + (x - 4)/12
Finding the common denominator, which is 12:
((2x + 3)(4/4) - (3x - 1)(6/6) + (x - 4)(1/1))/12
Simplifying the expression:
(4(2x + 3) - 6(3x - 1) + (x - 4))/12
Expanding and combining like terms:
(8x + 12 - 18x + 6 + x - 4)/12
Simplifying further:
(-9x + 14)/12
Therefore, the simplified expression is (-9x + 14)/12.
Remember, when simplifying algebraic expressions involving rational fractions, find a common denominator and then combine any like terms in the numerator.