College Algebra Attached is the problem in addition to my work so far. I submit

Question

College Algebra

Attached is the problem in addition to my work so far. I submit my answer online, since I am taking an online class.

I don’t understand why we ignore the 4 in:

4(x+6) (x-6)= 0

Why is there no solution?

x= 6 and x= -6. Need in depth explanation of this part especially.

Thank you.

lution(s) is/are_o (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution set is fx | x is a real number and x (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. There is no solution. 3. Solve. 4x 24 288 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution set is (x1 x is a real number and x (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) The solution(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O A. O. B. O C. There is no solution. 3/

Explanation / Answer

4x/x-6 -24/x+6= 288/(x^2-36)

Taking lcm we get (4x(x+6) -24(x-6))/(x^2-36)= 288/(x^2-36)

Since denominator is the same, it will be cancelled

4x^2+24x-24x+144= 288

4x^2=144

x^2= 36

So , we get x= +6 and -6

But if we substitute x = 6 or x= -6 in the LHS and RHS, the denominator becomes zero

And the expression becomes infinity and hence there is no solution.

Hence option c is correct, there is no solution.

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