Question

Solve :-
1/(x+3) + 1/(2x-1) = 11/(7x+9), x ≠ -3, 1/2, -9/7​

Answer 1

Answer

We have,

$\sf \dfrac{1}{(x + 3)} + \dfrac{1}{(2x - 1)} = \dfrac{11}{(7x + 9)}$

$\sf \dashrightarrow \dfrac{(2x - 1) + (x +3)}{(x + 3) (2x - 1)} = \dfrac{11}{(7x + 9)}$

$\sf \dashrightarrow \dfrac{(3x + 2)}{{2x}^{2} + 5x - 3} = \dfrac{11}{(7x + 9)}$

By cross multiplication,

$\dashrightarrow \sf (3x + 2) (7x + 9) = 11 ({2x}^{2} + 5x -3)$

$\sf \dashrightarrow {21x}^{2} + 41x + 18 = {22x}^{2} + 55x - 33$

$\sf \dashrightarrow {x}^{2} + 14x - 51 = 0$

$\sf \dashrightarrow {x}^{2} + 17x - 3x - 51 = 0$

$\sf \dashrightarrow x (x + 17) - 3 (x + 17) = 0$

$\sf \dashrightarrow (x + 17) (x - 3) = 0$

$\sf \dashrightarrow x + 17 = 0 \: \: or \: \: x = 3$

Thus, -17 and 3 are the roots of the given equation.