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Question Solve for all values of x: (1)/(x-4)+2=(4)/(x^2)-4x Answer Attemptiout of 2 (4) Additional Solution x=square

Pergunta

Question
Solve for all values of x:
(1)/(x-4)+2=(4)/(x^2)-4x
Answer Attemptiout of 2
(4) Additional Solution
x=square

Question Solve for all values of x: (1)/(x-4)+2=(4)/(x^2)-4x Answer Attemptiout of 2 (4) Additional Solution x=square

Solução

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LuizProfissional · Tutor por 6 anos

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To solve the equation, we first simplify the equation by multiplying both sides by $x^2 - 4x$ to get rid of the denominators:<br /><br />$x^2 - 4x = 4(x - 4) + 2x^2 - 8x$<br /><br />Simplifying further, we get:<br /><br />$x^2 - 4x = 4x - 16 + 2x^2 - 8x$<br /><br />Rearranging the terms, we get:<br /><br />$x^2 - 4x - 2x^2 + 4x + 16 = 0$<br /><br />Simplifying further, we get:<br /><br />$-x^2 + 16 = 0$<br /><br />Multiplying both sides by -1, we get:<br /><br />$x^2 - 16 = 0$<br /><br />Factoring the left side, we get:<br /><br />$(x - 4)(x + 4) = 0$<br /><br />Setting each factor equal to zero, we get two possible solutions:<br /><br />$x - 4 = 0$ or $x + 4 = 0$<br /><br />Solving for x, we get:<br /><br />$x = 4$ or $x = -4$<br /><br />However, substituting $x = 4$ back into the original equation, we get a denominator of zero, which is undefined. Therefore, the only solution is:<br /><br />$x = -4$
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