Respuesta :

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[tex]\frac{2a}{a^2+2a+1}+\frac{5}{a^2+4a+3}[/tex]

Factor the denominators.

[tex]\frac{2a}{\left(a+1\right)^2}+\frac{5}{\left(a+1\right)\left(a+3\right)}[/tex]

Adjust fractions based on LCM.

[tex]\frac{2a\left(a+3\right)}{\left(a+1\right)^2\left(a+3\right)}+\frac{5\left(a+1\right)}{\left(a+1\right)^2\left(a+3\right)}[/tex]

Denominators are same, so add the fractions.

[tex]\frac{2a\left(a+3\right)+5\left(a+1\right)}{\left(a+1\right)^2\left(a+3\right)}[/tex]

Expand the numerator.

[tex]\frac{2a^2+11a+5}{\left(a+1\right)^2\left(a+3\right)}[/tex]

Hi1315

Answer:

[tex]= \frac{2 {a}^{2} + 11a + 5}{ {(a + 1)}^{2}(a + 3)} \\ [/tex]

Step-by-step explanation:

[tex] \frac{2a}{ {a}^{2} + 2a + 1} + \frac{5}{ {a}^{2} + 4a + 3 } \\ \frac{2a}{(a + 1)(a + 1)} + \frac{5}{(a + 1)(a + 3)} \\ \frac{2a}{ {(a + 1)}^{2} } + \frac{5}{(a + 1)(a + 3)} \\ \frac{2a(a + 3) + 5(a + 1)}{ {(a + 1)}^{2}(a + 3) } \\ \frac{2 {a}^{2} + 6a + 5a + 5 }{ {(a + 1)}^{2}(a + 3)} \\ = \frac{2 {a}^{2} + 11a + 5}{ {(a + 1)}^{2}(a + 3)}[/tex]

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