Question

What two rational expressions sum to 3x+4/x^2-6x+5?

enter your answer so that each rational expression is in simplified form

(fill in the spots with question marks please)

3x+4/x^2-6x+5= ?/?(x-1)+?/?(x-5)

THE ANSWER IS:
-7/4(x-1)+ 19/4(x-5)

Answer 1

`(3x+4)/(x^2-6x+5)=(-7)/(4(x-1)) +(19)/(4(x-5))`

Explanation:

The given rational expression is:

`(3x+4)/(x^(2)-6x+5) = (3x+4)/((x-1)(x-5))`

We can use concept of Partial Fractions to solve this problem. Let,

`(3x+4)/((x-1)(x-5))=(A)/(x-1) +(B)/(x-5)`

Multiplying both sides by (x - 1)(x - 5), we get:

`3x+4=A(x-5)+B(x-1)`

Substituting x = 5, we get:

`3(5)+4=A(5-5)+B(5-1)\\\\ 15+4=0+4B\\\\ 19=4B\\\\ B=(19)/(4)`

Substituting x = 1, we get:

`3(1)+4=A(1-5)+B(1-1)\\\\ 7=-4A\\\\ A=-(7)/(4)`

Substituting the value of A and B, back in the original equation, we get:

`(3x+4)/(x^2-6x+5)=(-7)/(4(x-1)) +(19)/(4(x-5))`