How to simplify using partial fraction. 5/(x^2-5x+6) ?

We have to express the given expression 5/(x^2-5x+6) as
partial
fractions.

5/(x^2-5x+6)

=>
5 / ( x^2 - 3x - 2x + 6)

=> 5/ ( x(x - 3) - 2( x -
3))

=> 5/ (x - 2)(x -
3)

=> A / (x - 2) + B/ (x -
3)

=> [A(x - 3) + B(x - 2)]/ (x - 2)(x
-3)

Ax - 3A + Bx - 2B =
5

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

Equate the coefficients of x and the numeric
coefficients

=> A + B = 0 and 3A + 2B =
-5

=> A = -B

Substitute
in 3A + 2B = -5

=> -3B + 2B =
-5

=> B = 5

A =
-5

We can write 5/(x^2-5x+6) = 5/(x - 3) -
5/(x - 2).