Question

Find the value of A that makes the following equation true for all values of x:3x− 3/x^2 =A⋅3x

A.A=−1
B. A=0
C.A=1
D. A=2

Answer 1

To find the value of A that makes the equation true for all values of x, rearrange the equation and solve for A. A depends on the value of x, so there is no single value of A that will make the equation true for all values of x.

Step-by-step explanation:

To find the value of A that makes the equation true for all values of x, we need to rearrange the equation and solve for A.

Start by multiplying both sides of the equation by x^2 to get rid of the fraction: 3x^3 - 3 = A * 3x^2.

Next, rearrange the equation to isolate A: A = (3x^3 - 3) / (3x^2).

Now we can see that A depends on the value of x, so there is no single value of A that will make the equation true for all values of x. Therefore, the correct answer is none of the given options: A is not equal to -1, 0, 1, or 2.