UPSC CDS 2 2021 Math Paper

Given,
A+B=‌

x2−8

x+2

... (i)
and A−B=‌

−x2+2x+4

x+2

. . . (ii)
By Eq. (i) - Eq. (ii), we get
(A+B)−A−B)
=‌

x2−8

x+2

−‌

(−x2+2x+4)

x+2

⇒2B=‌

x2−8−(−x2+2x+4)

x+2

⇒2B=‌

x2−8+x2−2x−4

x+2

⇒2B=‌

2x2−2x−12

x+2

⇒B=‌

x2−x−6

x+2

=‌

x2−3x+2x−6

x+2

=‌

(x−3)(x+2)

(x+2)

=x−3
‌ Option (c) is ‌‌

2x2−7x+3

2x−1

On solving this further, we get
‌‌=‌

2x2−6x−x+3

2x−1

‌‌=‌

2x(x−3)−1(x−3)

(2x−1)

‌‌=‌

(2x−1)(x−3)

(2x−1)

=x−3
Since, value of B and option (c) represents the same value.
Hence, B is equal to ‌

2x2−7x+3

2x−1

.