If the expression 4x^2/2x-1 is written in the equivalent form 1/2x-1+A, what is A in terms of x?
A) 2x+1
B) 2x-1
C) 4x^2
D) 4x^2-1
Maybe you mean ????
If the expression 4x^2/(2x-1) is written in the equivalent form 1/(2x-1)+A, what is A in terms of x?
4x^2/(2x-1) = 1/(2x-1) + A
A = (4x^2-1)/(2x-1)
A = (2x-1)(2x+1)/(2x-1)
A = 2x+1
You are welcome.
thank you so much +Damon +scott
yes ... you're welcome
4x^2 / 2x-1 = (1 / 2x-1) + A
subtracting (1 / 2x-1) ... (4x^2 - 1) / (2x-1) = A
factoring ... [(2x+1) (2x-1)] / (2x-1) = A
cancel quantities where appropriate
To find the value of A in the expression 4x^2/(2x-1) expressed as 1/(2x-1) + A, we need to rewrite the original expression 4x^2/(2x-1) as a single fraction with a common denominator.
First, we'll rewrite the expression as (4x^2)/(2x-1).
To add fractions, we need a common denominator. In this case, the common denominator is (2x-1).
To get the first fraction with the denominator (2x-1), we need to multiply the numerator 4x^2 by (2x-1) and the denominator by (2x-1):
(4x^2)/(2x-1) = (4x^2 * (2x-1))/(2x-1) = (8x^3 - 4x^2)/(2x-1)
Now, we can express this as the sum of 1/(2x-1) and some value A:
(8x^3 - 4x^2)/(2x-1) = 1/(2x-1) + A
Comparing the numerators on both sides, we have:
8x^3 - 4x^2 = 1 + A * (2x-1)
To find the value of A, we need to isolate it. First, simplify the right side of the equation:
8x^3 - 4x^2 = 1 + 2Ax - A
Rearranging the terms:
8x^3 - 4x^2 - 2Ax + A = 1
Now, we can compare coefficients. On the left side, we have:
8x^3 = coefficient of x^3
-4x^2 = coefficient of x^2
-2A = coefficient of x
On the right side, we have:
1 = constant term
Comparing the coefficients, we can determine that the coefficient of x^3 on both sides is 8, which means that it must be equal to 0 on the right side. Therefore:
8 = 0
Since 8 does not equal 0, this equation is not possible and the answer is not valid.
Therefore, the value of A cannot be determined in terms of x.