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and combine to one fraction. (5x+7)/(x-4)+(3)/(x)

Pergunta

and combine to one fraction.
(5x+7)/(x-4)+(3)/(x)

and combine to one fraction. (5x+7)/(x-4)+(3)/(x)

Solução

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AugustoVeterano · Tutor por 9 anos

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To combine the given fractions into one, we need to find a common denominator. The denominators are \(x-4\) and \(x\). The least common denominator (LCD) is \(x(x-4)\).<br /><br />Rewrite each fraction with the LCD as the denominator:<br /><br />\[<br />\frac{5x+7}{x-4} = \frac{(5x+7)x}{x(x-4)} = \frac{5x^2 + 7x}{x(x-4)}<br />\]<br /><br />\[<br />\frac{3}{x} = \frac{3(x-4)}{x(x-4)} = \frac{3x - 12}{x(x-4)}<br />\]<br /><br />Now, add the two fractions:<br /><br />\[<br />\frac{5x^2 + 7x}{x(x-4)} + \frac{3x - 12}{x(x-4)} = \frac{5x^2 + 7x + 3x - 12}{x(x-4)}<br />\]<br /><br />Combine like terms in the numerator:<br /><br />\[<br />\frac{5x^2 + 10x - 12}{x(x-4)}<br />\]<br /><br />So, the combined fraction is:<br /><br />\[<br />\frac{5x^2 + 10x - 12}{x(x-4)}<br />\]
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