The fractionB3x1 is subtracted from the fraction A2x3. The resulting fraction is11(2x3)(3x1). Then find A + B.
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Given : Fraction B/(3x - 1 ) is subtracted from the fraction A/(2x + 3)
. The resulting fraction is -11/(2x + 3)(3x - 1).
To Find : A + B =
Solution:
A/(2x + 3) - B/(3x - 1 )
= A(3x - 1) - B(2x + 3)
= (3Ax - A - 2BX - 3B)/(2x + 3)(3x - 1)
(3Ax - A - 2BX - 3B)/(2x + 3)(3x - 1) = 11/(2x + 3)(3x - 1).
3Ax - A - 2BX - 3B = - 11
=> x(3A - 2B) - (A + 3B) = - 11
Comparing
3A - 2B = 0 Eq1
A + 3B = 11 Eq2
3* Eq1 + 2*Eq3
=> 9A + 2A = 22
=> 11A = 22
=> A = 2
2 + 3B = 11
=> 3B = 9
=> B = 3
A + B = 2 + 3 = 5
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