Which expression is equivalent to (8x − 2/x + 3)(6 − x/x + 2)?
A. 56x^2 + 14x/x^2 + 5
B. 56x^2 + 14x/x^2+5x+6
C. −8x^2 + 50x − 12/2x + 5
D. −8x^2 + 50x − 12/ x^2+5x+6
D i meant sorry !
To simplify the given expression, we can follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).
Let's simplify each part of the expression individually:
1. Simplify the first part:
(8x − 2/x + 3)
To simplify this part, we can distribute the numerator (8x − 2) over the denominator (x + 3):
(8x − 2)/(x + 3) = (8x)/(x + 3) − (2)/(x + 3) = 8x/(x + 3) − 2/(x + 3)
2. Simplify the second part:
(6 − x/x + 2)
Here, we have to determine if x is in the numerator or denominator of (x + 2). To clarify, let's add parentheses:
(6 − (x/x + 2))
Now, we can simplify:
(x/x + 2) = 1 + 2 = 3
So, the second part simplifies to:
(6 − x/x + 2) = 6 − 3 = 3
Now, let's simplify the entire expression by multiplying the simplified parts together:
(8x/(x+3) - 2/(x+3))(3)
Multiplying by 3:
3 * (8x/(x+3) - 2/(x+3)) = (24x/x+3) - (6/(x+3)) = (24x - 6) / (x+3)
Therefore, the equivalent expression is (24x - 6) / (x+3), which matches option C.
So, the correct answer is C. −8x^2 + 50x − 12/2x + 5.