3-3x - 12x - 3- - 2 -2x - 33x -1- - 5- x -13- -32

Given #160; 3(3x 12x+3) 2(2x+33x 1)=5 9x 32x+3 + 4x 63x 1=5 (9x 3)(3x 1)+(2x+3)( 4x 6)=5(2x+3)(3x 1) 27x^2 9x 9x+3 8x^2 12x 12x 18=5(6x^2 ...

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Byju's Answer

Standard XII

Mathematics

Composite Function

3[3x - 12x + ...

Question

$3 [\frac{3 x - 1}{2 x + 3}] - 2 [\frac{2 x + 3}{3 x - 1}] = 5; x \neq \frac{1}{3}, - \frac{3}{2}$

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Solution

Given
$3 (\frac{3 x - 1}{2 x + 3}) - 2 (\frac{2 x + 3}{3 x - 1}) = 5$
$\frac{9 x - 3}{2 x + 3} + \frac{- 4 x - 6}{3 x - 1} = 5$
$⟹ (9 x - 3) (3 x - 1) + (2 x + 3) (- 4 x - 6) = 5 (2 x + 3) (3 x - 1)$
$27 x^{2} - 9 x - 9 x + 3 - 8 x^{2} - 12 x - 12 x - 18 = 5 (6 x^{2} - 2 x + 9 x - 3)$
$19 x^{2} - 42 x - 15 = 30 x^{2} + 35 x - 15$
$11 x^{2} + 77 x = 0$
$x (11 x + 77) = 0$
$x = 0, x = - 7$

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$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$