Simply the following rational equation

(x-5/x

^{2}-25) - (3/x+5)= A/Bwhere A and B are polynomials of degree as low as possible and the leading coefficient of B is 1.

A=

B=

Simply the following rational equation

(x-5/x^{2}-25) - (3/x+5)= A/B

where A and B are polynomials of degree as low as possible and the leading coefficient of B is 1.

A=

B=

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Middletown, CT

Hi Dalia;

(x-5/x^{2}-25) - (3/x+5)= A/B

I think this is...

[(x-5)/(x^{2}-25)]-[3/(x+5)]=A/B

(x^{2}-25)=(x+5)(x-5)

{(x-5)/[(x+5)(x-5)]}-[3/(x+5)]=A/B

In the first bracketed equation, the (x-5) in the numerator and denominator cancel...

{(x-5)/[(x+5)(x-5)]}-[3/(x+5)]=A/B

[1/(x+5)]-[3/(x+5)]=A/B

Let's combine numerators...

(1-3)/(x+5)=A/B

-2/(x+5)=A/B

For B to be a polynomial with a leading coefficient of 1, then in such equation, the vertex is...

-b/2a=1

The easiest resolution for this is...

-b=4, b=-4

2a=4, a=2

2x^{2}-4x+?

(2x-14)(x+5)

-2/(x+5)=A/B

Let's multiply the top and bottom of the left side by (2x-14)

[-2(2x-14)]/[(x+5)(2x-14)]=A/B

-2(2x-14)

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