Fsc Part 1 Mathematics (Complete Solution)

Q8
Solve the Following equations by factorization

a
ax - 1
+
b
bx - 1
= a + b
Solution
a
ax - 1
- b +
b
bx - 1
- a = 0
a - b(ax - 1)
ax - 1
+
b - a(bx - 1)
bx - 1
= 0
a - abx + b
ax - 1
+
b - abx + a
bx - 1
= 0
a - abx + b
ax - 1
+
a - abx + b
bx - 1
= 0
(a - abx + b) (
1
ax - 1
+
1
bx - 1
) = 0
Either     a - abx + b = 0      OR     
1
ax - 1
+
1
bx - 1
= 0
abx = a + b bx - 1 + ax - 1 = 0
x =
a + b
ab
bx + ax - 2 = 0
x =
a + b
ab
x(a + b) = 2
x =
a + b
ab
x =
2
a + b



Solution Set     {
a + b
ab
,
2
a + b
}

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