What is the quotient of x+ 4/ x-1 / x^2 + x/x-1.
A. x + 4 / x ( x + 1 )
B. x + 4 / ( x - 1 ) ^2
C. 1 / x
D. x^2 + 4 x + 4 / 2 x
My answer I pick was ( A.)
What the sum of x / 3 x - 6 + 1 / 8
A. x / 24 ( x - 2 )
B. 1 + x / 3 x + 2
C. x / 24 x - 48
D . 11 x - 6 / 24 ( x - 2 )
My answer I was not sure I came up with two answer ( C and D )
1)
i interpreted it as:
[(x+4)/(x-1)] / [(x^2 + x)/(x-1)]
therefore,
(x+4)/(x-1) * (x-1)/(x(x+1))
(x+4)/(x(x+1))
letter A
2)
i interpreted it as:
x / (3 x - 6) + 1 / 8
therefore,
(8x + 3x - 6) / 8(3x - 6)
(11x - 6) / (24x - 48)
letter D
Thank you Monkey D Luffy
To find the quotient of the given expression, x + 4 / x - 1 / x^2 + x / x - 1, you need to follow the order of operations (PEMDAS) and simplify the expression.
Let's break it down step by step:
1. Simplify the numerator of the first fraction: x + 4.
2. Simplify the denominator of the first fraction: x - 1.
3. Simplify the numerator of the second fraction: x^2 + x.
4. Simplify the denominator of the second fraction: x - 1.
Now, to combine the two fractions, remember that dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as:
(x + 4) / (x - 1) * (x - 1) / (x^2 + x)
Next, cancel out the common factor (x - 1) in the numerator and denominator:
(x + 4) / (x^2 + x)
The final simplified expression is (x + 4) / (x^2 + x).
Comparing this to the answer choices, we can see that the correct choice is A. (x + 4) / (x (x + 1)) since it matches the simplified expression.
For the second question, let's simplify the expression x / 3x - 6 + 1 / 8:
1. Simplify the first term: x / (3x - 6).
2. Simplify the second term: 1 / 8.
To combine the two terms, we need a common denominator.
The common denominator is 8(3x - 6). To achieve this, we multiply the first term by (8 / 8) and the second term by [(3x - 6) / (3x - 6)]:
(8x / 8(3x - 6)) + (1(3x - 6) / 8(3x - 6))
Simplifying each term, we get:
x / (3x - 6) + (3x - 6) / (8(3x - 6))
To combine these terms, we need a common denominator, which is 8(3x-6):
(x + (3x - 6)) / (8(3x - 6))
(4x - 6) / (8(3x - 6))
Now, simplifying further, we can divide 2 from the numerator and denominator:
2(2x - 3) / 2(4(3x - 6))
(2x - 3) / (4(3x - 6))
The final simplified expression is (2x - 3) / (12x - 24).
Now, let's compare this with the answer choices:
A. x / (24(x - 2)) - This does not match the simplified expression.
B. 1 + x / (3x + 2) - This does not match the simplified expression.
C. x / (24x - 48) - This matches the simplified expression.
D. (11x - 6) / (24(x - 2)) - This does not match the simplified expression.
Therefore, the correct choice is C. x / (24x - 48).