Decompose into partial fractions : (5x + 10) /x ( x +5)

We need to write as partial fractions as
follow:

(5x+10)/x(x+5) = A/x +
B/(x+5)

We will multiply by x(x+5) both
sides.

==> A(x+5) + Bx = 5x +
10

Now we will group similar
terms.

==> Ax + 5A + Bx = 5x +
10

==> (A+B)x + 5A = 5x +
10

Now we will
compare;

==> 5A = 10 ==> A =
2

==> A+B = 5 ==> B = 5 - A = 5-2=
3

==> B = 3

Now we will
substitute into the
equation.

==>
(5x+10)/x(x+5) = (2/x) + 3/(x+5)