The equation (24x2+25x−47/ax−2)=−8x−3−(53/ax−2) is true for all values of x≠(2/a), where a is a constant.
What is the value of a?
A) -16
B) -3
C) 3
D) 16
No, not grade 5 :)
Holy toledo! This is fifth grade math?! Yikes!
Do you mean?
(24x^2+25x−47) /(ax−2)=−8x−3−[53/(ax−2)]
if so
24x^2+25x−47 = (ax−2)(-8x-3) -53
24x^2+25x−47 = -8ax^2 +16x -3ax +6 - 53
32 x^2 + (9+3a)x = 0
x(32 x +9 +3a) = 0
3 a = - 9 - 32x
I have an error or problem has a typo
I bet it is supposed to be 3 a = -9
or a =-3
(24x^2+25x−47) /(ax−2)=−8x−3−[53/(ax−2)]
if it were
(24x^2+25x−47) /(ax−2)=+8x−3−[53/(ax−2)]
then the x^2 term would go away later and the a=-3 would be perfect.
typo I am sure
OH
24x^2+25x−47 = -8ax^2 +16x -3ax +6 - 53
(24 +8a) x^2 + (9+3a)x = 0
a =-3 makes both = 0
To find the value of "a" that satisfies the given equation, we need to solve for "a" by setting up an equation and simplifying it.
Given equation: (24x^2 + 25x - 47)/(ax - 2) = -8x - 3 - (53/(ax - 2))
Step 1: Simplify the right side of the equation by combining like terms.
-8x - 3 - 53/(ax - 2) = (-8x - 3)(ax - 2) - 53/(ax - 2)
Step 2: Simplify the left side of the equation by multiplying both sides by (ax - 2) to eliminate the denominator.
(ax - 2) * (24x^2 + 25x - 47)/(ax - 2) = (-8x - 3)(ax - 2) - 53/(ax - 2)
This will give us an equation without any denominators.
Step 3: Simplify further by distributing and combining like terms to isolate the variable "a".
24x^2 + 25x - 47 = (-8x - 3)(ax - 2) - 53/(ax - 2)
Expand the right side:
24x^2 + 25x - 47 = -8ax^2 + 16x - 3ax + 6 - 53/(ax - 2)
Now, combine like terms:
24x^2 + 25x - 47 = -8ax^2 + (16x - 3ax) + (6 - 53/(ax - 2))
Within the parentheses, combine like terms:
24x^2 + 25x - 47 = -8ax^2 + (13x - 3ax) + (6 - 53/(ax - 2))
Combine the x terms:
24x^2 + 25x - 47 = -8ax^2 + 10x + (6 - 53/(ax - 2))
Multiply through by (ax - 2):
(24x^2 + 25x - 47)(ax - 2) = (-8ax^2 + 10x + (6 - 53/(ax - 2)))(ax - 2)
Expand and simplify:
24ax^3 - 48x^2 + 25ax^2 - 50x - 47ax + 94 = -8a^2x^3 + 16ax^2 + 6ax - 16x - 53
Combine like terms:
24ax^3 - 48x^2 + 25ax^2 - 50x - 47ax + 94 = -8a^2x^3 + 16ax^2 + 6ax - 16x - 53
Let's compare the coefficients of x^3 on both sides:
24a = -8a^2
Divide both sides by 8a:
3 = -a
Multiply by -1 to isolate "a":
a = -3
Therefore, the value of "a" that satisfies the equation is -3.
The answer is B) -3.