Question

The equivalent perial fraction of (x+1-35 А B *+1 6-31 AB C A B-C (c *+1 1-3 6-3​

Answer 1

Step-by-step explanation:

x2+5x+7=x−3A+(x−3)2B+(x−3)3C

x2+5x+7=A(x−3)2+B(x−3)+C

x2+5x+7=A(x2+9−6x)+B(x−3)+C

x2+5x+7=Ax2+(B−6A)x+(9A−3B+C)

Comparing the coefficient of same powers of xon both sides, we have

A=1

B−6A=5

⇒B=6+5=11

9A−3B+C=7

⇒9−33+C=7

⇒C=31

Substituting the value of A,B and C in equation (1), 

We get

(x−3)3