Respuesta :

Answer:

  • [tex]C)~A+ \frac{B}{x-3} +\frac{c}{(x-3)^2}[/tex]

Step-by-step explanation:

→ [tex]\frac{(7x^2-40x+52)}{(x^2-6x+9)}[/tex]

→ [tex]\frac{7x^2-40x+52}{x^2-2.3x+(3)^2}[/tex]

→  [tex]\frac{7x^2-40x+52}{(x-3)^2}[/tex]

So, your answer is C

[tex]----------[/tex]

hope it helps...

have a great day!!

The partial fractions is to start with the simplified, and "decompose" the expression into initial polynomial fractions, and the calculation is as follows:

Partial fractions:

  • The degree of the fraction must be strictly less than the degree of the denominator required to conduct partial fractions.
  • It's critical to keep that in mind. So, once we've established that partial fractions are possible, we factor the denominator to the greatest extent possible.

[tex]\to \frac{7x^2-40x+52}{x^2-6x+9}\\\\\to \frac{7x^2-40x+52}{x^2-(3x-3x)+9}\\\\\to \frac{7x^2-40x+52}{x^2-3x+3x+9}\\\\\to \frac{7x^2-40x+52}{x(x-3)+3(x+3)}\\\\\to \frac{7x^2-40x+52}{(x-3)^2}\\\\\to \frac{7x^2-40x+52}{(x-3)^2}\\\\\to A+ \frac{B}{(x-3)}+\frac{C}{(x-3)^2}\\\\[/tex]

Find out more about the partial fractions here:

brainly.com/question/24594390

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