Question

resolve into partial fractions 1÷3x^2+13x-10​

Answer 1

Answer:

Step-by-step explanation:

On dividing we get

x3−2x2−13x−12x2−3x−10=(x+1)−2(x2−3x−10)

Let2(x2−3x−10)=2(x−5)(x+2)=Ax−5+Bx+2

then,2(x−5)(x+2)+A(x+2)+B(x−5)(x−5)(x+2)

or 2≡A(x+2)+B(x−5).

putting (x−5)=0orx=5in (ii) , we get A=(2/7)

Putting (x+2)=0orx=−2in (ii) , we get B=(−2/7)

∴2(x2−3x−10)=27(x−5)−27(x+2).

hence,x3−2x2−13x−12x2−3x−10=(x+1)−27(x−5)+27(x+2).