Fsc Part 1 Mathematics (Complete Solution)

Q6
Solve the Following equations by factorization

x
x + 1
+
x + 1
x
=
5
2
; x ≠ -1, 0
x
x + 1
+
x + 1
x
-
5
2
= 0
(2x)x + 2(x + 1)(x + 1) - 5 (x(x + 1))
2(x)(x + 1)
= 0
2x2 + 2(x2 + 2x + 1) - 5 (x2 + x)
2(x)(x + 1)
= 0
2x2 + 2x2 + 4x + 2 - 5x2 - 5x
2(x)(x + 1)
= 0
-x2 - x + 2
2(x)(x + 1)
= 0
-x2- x + 2 = 0
[∴ Multiply both sides by 2(x)(x + 1)]
x2+ x - 2 = 0
[∴ Multiply both sides by -1]
x2+ 2x - x - 2 = 0
[∴ 2 x (-1) = -2 and 2 + (-1) = 1]
x(x + 2) - 1(x + 2) = 0
(x - 1)(x + 2) = 0
Either x - 1 = 0      OR      x + 2 = 0
x = 1 x = -2
∴ Soution Set = { 1, -2 }

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