Solve the rational equation. Be sure to check for extraneous solutions. (Enter y

Question

Solve the rational equation. Be sure to check for extraneous solutions. (Enter your answers as a comma-separate list. If their solution, enter NO SOLUTION.) 1/x + 4 + 1/x - 4 = x^2 - 24/x^2 - 16 x = Solve the rational equation. Be sure to check for extraneous solutions. (Enter your answers as a comma-separated list. If their solution, enter NO SOLUTION.) 6x + 30/x + 1 = x + 2 Solve the rational equation. Be sure to check for extraneous solutions, (Enter your answers as a comma-separated list. If their solution, enter NO SOLUTION.)

Explanation / Answer

1/(x +4) + 1/( x -4) = (x^2 - 24)/(x^2 - 16)

LHS :( 2x )/(x^2 -16)

( 2x )/(x^2 -16) = (x^2 - 24)/(x^2 - 16)

2x = x^2 -24

x^2 - 2x - 24 =0

x^2 -6x +4x -24 =0

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

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

x = -4 , 6

x = -4 is not a solution , it is an extraneous solution

So, x = 6 solution

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