Pergunta

(x)/(x^2)+4x-45cdot (x^2+13x+36)/(x+4) pti ont of
Solução

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JoanVeterano · Tutor por 9 anos
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To simplify the given expression, we need to factorize the numerator and denominator of each fraction and then cancel out common factors.<br /><br />The given expression is:<br />$\frac {x}{x^{2}+4x-45}\cdot \frac {x^{2}+13x+36}{x+4}$<br /><br />First, let's factorize the denominator of the first fraction:<br />$x^{2}+4x-45 = (x+9)(x-5)$<br /><br />Now, the expression becomes:<br />$\frac {x}{(x+9)(x-5)}\cdot \frac {x^{2}+13x+36}{x+4}$<br /><br />Next, let's factorize the numerator of the second fraction:<br />$x^{2}+13x+36 = (x+9)(x+4)$<br /><br />Now, the expression becomes:<br />$\frac {x}{(x+9)(x-5)}\cdot \frac {(x+9)(x+4)}{x+4}$<br /><br />We can cancel out the common factors $(x+9)$ and $(x+4)$:<br />$\frac {x}{(x-5)}$<br /><br />Therefore, the simplified form of the given expression is $\frac {x}{x-5}$.
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