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How do you solve #x/(x+4) - 4/(x-4) = (x^2+16)/(x^2-16)#?

Answer 1

NO SOLUTIONS!!!!

Consider as common denominator #x^2-16=(x-4)(x+4)#: #(x(x-4)-4(x+4))/cancel((x^2-16))=(x^2+16)/cancel((x^2-16))# #cancel(x^2)-4x-4x-16=cancel(x^2)+16# #-8x=32# #x=-4# BUT this value cannot be accpeted because it makes the denominator of my original expression equal to ZERO!!! So...NO real solutions!!!!

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Answer 2

Ethan Adkins

To solve the equation x/(x+4) - 4/(x-4) = (x^2+16)/(x^2-16), we can follow these steps:

Start by finding a common denominator for all the fractions involved. In this case, the common denominator is (x+4)(x-4).
Multiply each term by the common denominator to eliminate the fractions.
Simplify the equation by distributing and combining like terms.
Continue simplifying until you have a quadratic equation.
Solve the quadratic equation by factoring, using the quadratic formula, or completing the square.
Check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

By following these steps, you can find the solution(s) to the given equation.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.