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# Simplify this rational expression

Simply the following rational equation
(x-5/x2-25) - (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=

### 1 Answer by Expert Tutors

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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Hi Dalia;
(x-5/x2-25) - (3/x+5)= A/B
I think this is...
[(x-5)/(x2-25)]-[3/(x+5)]=A/B
(x2-25)=(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
2x2-4x+?
(2x-14)(x+5)
2x2-10x-70.......This is the B equation.
-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)
-4x+28.........This is the A equation.