5 Write the partial fraction decomposition of x 5 x 3 Solu

5. Write the partial fraction decomposition of (x - 5) (x + 3)

Solution

5. x/(x-5)(x+3) = A/(x-5) + B/(x+3)

x= A(x+3)+B(x-5)

x=x(A+B) +3A-5B

A+B=1 and 3A-5B=0

A=5/8, B=3/8

So the required partial decomposition is 5/8(x-5) + 3/8(x+3)

8. Center(h,k)=(0,0)

Focus(h+c,k)=(3,0)

Therefore c=3

Vertex(h+a,k)=(5,0)

Therefore a=5

b²=a²-c²=16

x²/25 +y²/16=1