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Solve for all values of x. (2)/(x+5)+(5)/(x-5)=(x)/(x-5) Answer Attemptiout of 2 Additional Solution (C) No Solution x=square

Pergunta

Solve for all values of x.
(2)/(x+5)+(5)/(x-5)=(x)/(x-5)
Answer Attemptiout of 2
Additional Solution (C) No Solution
x=square

Solve for all values of x. (2)/(x+5)+(5)/(x-5)=(x)/(x-5) Answer Attemptiout of 2 Additional Solution (C) No Solution x=square

Solução

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ElvisElite · Tutor por 8 anos

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To solve the equation, we first find a common denominator for the fractions on the left side of the equation, which is (x+5)(x-5). Then we multiply both sides of the equation by this common denominator to eliminate the fractions:<br /><br />2(x-5) + 5(x+5) = x(x+5)<br /><br />Expanding and simplifying the equation gives:<br /><br />2x - 10 + 5x + 25 = x^2 + 5x<br /><br />Combining like terms gives:<br /><br />7x + 15 = x^2 + 5x<br /><br />Rearranging the equation gives:<br /><br />x^2 - 2x - 15 = 0<br /><br />Factoring the quadratic equation gives:<br /><br />(x - 5)(x + 3) = 0<br /><br />Setting each factor equal to zero gives the solutions:<br /><br />x = 5 or x = -3<br /><br />However, substituting x = 5 back into the original equation, we find that it makes the denominator of the second fraction zero, which is undefined. Therefore, the only solution is:<br /><br />x = -3
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