Fsc Part 1 Mathematics (Complete Solution)

Q7
Solve the Following equations by factorization

1
x + 1
+
2
x + 2
=
7
x + 5
; x ≠ -1, -2, -5
Solution
1
x + 1
+
2
x + 2
=
7
x + 5
Multiply Both sides by (x + 1)(x + 2)(x + 5)
1(x + 1)(x + 2)(x + 5)
x + 1
+
2(x + 1)(x + 2)(x + 5)
x + 2
=
7(x + 1)(x + 2)(x + 5)
x + 5
1(x + 2)(x + 5) + 2(x + 1)(x + 5) = 7(x + 1)(x + 2)
(x2 + 5x + 2x + 10) + 2(x2 + 5x + x + 5) = 7(x2 + 2x + x + 2)
(x2 + 7x + 10) + 2(x2 + 6x + 5) = 7(x2 + 3x + 2)
x2 + 7x + 10 + 2x2 + 12x + 10 = 7x2 + 21x + 14
3x2 + 19x + 20 = 7x2 + 21x + 14
7x2 + 21x + 14 - 3x2 - 19x - 20 = 0
4x2 + 2x - 6 = 0



4x2+ 6x - 4x - 6 = 0
[∴ 6 x (-4) = 24 and 6 - 4 = 2
2x( 2x + 3) - 2(2x - 3) = 0
(2x - 2)( 2x + 3) = 0



Either 2x - 2 = 0      OR      2x + 3 = 0
2x = 2 2x = -3
x =
2
2
x = -
3
2
x = 1 x = -
3
2



∴ Solution Set = {1, -
3
2
}

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