Question

If $\frac{(1+x)(1+2x)(1+3x)}{(1-x)(1-2x)(1-3x)}=K+$ $\frac{A}{1-x}+\frac{B}{1-2x}+\frac{C}{1-3x}$, then which of the following is correct

• A. $K=6$
• B. $A=12$
• C. $B=30$
• D. $C=-20$

Answer 1

The correct option is B $A=12$

$LHS=\frac{(1+x)(1+2x)(1+3x)}{(1-x)(1-2x)(1-3x)}$
$RHS=k(1-x)(1-2x)(1-3x)+A(1-2x)(1-3x)$
$+B(1-x)(1-3x)$
$+C(1-x)(1-2x)$
$(1-x)(1-2x)(1-3x)$
$LHS=RHS$
$(1+x)(1+2x)(1+3x)=k(1-x)(1-2x)(1-3x)+A(1-2x)(1-3x)$
$+B(1-x)(1-3x)$
$+C(1-x)(1-2x)$
for the value of k equating the co- efficients
of $x^3$ So, $k=-1$
for the value of A put $x=1;A=12$
for the value of B put $x=1/2;B=-30$
for the value of C put $x=1/3;C=10$
So, $k=-1,A=12;B=-30$
$c=10$