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Please show me how to solve this problem.

8/x^2-16 + 3/4 = 1/x-4

multiply each of the terms by x^2, collect your like terms and bring them all to the left side.
You will have a quadratic equation.

BTW, since you did not use brackets I will assume your last term is (1/x)-4
and not 1/(x-4), otherwise the solution process would change.

looking at your equation and the values again, you probably meant:

8/(x^2-16) + 3/4 = 1/(x-4)

in that case, notice that x^2-16 factors into (x+4)(x-4)

so multiply each term by 4(x+4)(x-4), which will clear all your denominators, and you will have a quadratic.

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