Hi Dalia;
(x5/x^{2}25)  (3/x+5)= A/B
I think this is...
[(x5)/(x^{2}25)][3/(x+5)]=A/B
(x^{2}25)=(x+5)(x5)
{(x5)/[(x+5)(x5)]}[3/(x+5)]=A/B
In the first bracketed equation, the (x5) in the numerator and denominator cancel...
{(x5)/[(x+5)(x5)]}[3/(x+5)]=A/B
[1/(x+5)][3/(x+5)]=A/B
Let's combine numerators...
(13)/(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+?
(2x14)(x+5)
2x^{2}10x70.......This is the B equation.
2/(x+5)=A/B
Let's multiply the top and bottom of the left side by (2x14)
[2(2x14)]/[(x+5)(2x14)]=A/B
2(2x14)
4x+28.........This is the A equation.
Feb 4

Vivian L.