Question

a) $\frac{x}{x - 3} - \frac{2}{x {}^{2} - 9 }$

b)$\frac{2x}{ {x}^{2} - 2x - 15 } + \frac{3}{x {}^{2} - 10x + 25}$

peço ajuda nessas simplificações, por favorrr gente.

Answer 1

Olá Ilda :)
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• Casos notáveis

$\boxed{\boxed{\mathsf{a^2 - b^2 = (a -b)(a + b) } }}}$
$\boxed{\boxed{\mathsf{(a \pm b)^2 = a^2 \pm 2ab + b^2 } }}}$
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a) $\: \: \: \mathsf{\dfrac{x}{x - 3} - \dfrac{2}{x^2 - 9 } }$

$\mathsf{\dfrac{x}{x - 3} - \dfrac{2}{x^2 - 3^2 } }$

✦ Usando a propriedade dos casos notáveis, teremos,

$\mathsf{ \underset{(x + 3)}{\dfrac{x}{x - 3}} - \dfrac{2}{(x - 3)(x + 3) } }$

$\mathsf{ \dfrac{x(x + 3) - 2}{(x - 3)(x + 3) } }$

$\boxed{\boxed{ \mathsf{ \dfrac{x^2 + 3x - 2}{x^2 - 9} }}}} \end{array}\qquad\checkmark$

$b) \: \: \: \mathsf{\dfrac{2x}{ {x}^{2} - 2x - 15 } + \dfrac{3}{x^{2} - 10x + 25}}$

$\mathsf{\dfrac{2x}{ (x - 5)(x + 3) } + \dfrac{3}{(x - 5)(x - 5)}}$

$\mathsf{ \overset{\dfrac{2x}{ (x - 5)(x + 3) }}{(x - 5 )} \overset{ + \dfrac{3}{(x - 5)(x - 5)}}{(x + 3)}}$

$\mathsf{\dfrac{2x(x - 5)+ 3(x + 3)}{ (x - 5)^2(x + 3)} }$

$\mathsf{\dfrac{2x^2 - 10x + 3x + 9)}{ (x - 5)^2(x + 3)} }$

$\mathsf{\dfrac{2x^2 - 7x + 9)}{ (x - 5)^2(x + 3)} }$

$\boxed{\boxed{ \mathsf{\dfrac{2x^2 - 7x + 9}{ x^3 - 7x^2 -5x + 75} }}}}\end{array}\qquad\checkmark$


Espero ter colaborado!
Óptimos estudos :)
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