Certainly, let's solve the problems step by step.
Problem 1:
24x^(2 power) + 25r - 47 / ax - 2 = 8x - 3 - 53 / ax - 2
We can see that the denominators ax-2 are the same on both sides. So, we can multiply both sides by ax-2 to get rid of the fractions:
24x^(2 power) + 25r - 47 = 8x(ax-2) - 3(ax-2) - 53
Expanding the right side:
24x^(2 power) + 25r - 47 = 8ax^2 - 16x - 3ax + 6 - 53
Combining like terms:
24x^(2 power) + 25r - 47 = 5ax^2 - 19x - 47
Now, we can equate the coefficients of corresponding powers of x:
24 = 5a
25r = -19
From the first equation, we get a = 24/5.
From the second equation, we get r = -19/25.
Therefore, A = a + r = 24/5 - 19/25 = 119/25.
Problem 2:
3x - y = 12
We want to find the value of 8x / 2y. Let's first express y in terms of x from the given equation:
y = 3x - 12
Now, substituting this value of y in the expression we want to find:
8x / 2y = 8x / 2(3x - 12) = 4x / (3x - 12)
We cannot simplify this expression further without knowing the value of x. So, t