Solve for x- 2-x-1-3-2x-2-23-5 x

2/x+1 + 3/2(x 2) = 23/5x 4(x 2)+3(x+1)/2(x+1)(x 2)=23/5x 5x(4(x 2) + 3(x+1))=46(x+1)(x 2) 11x^2 21x 92=0 11x^2 44x+23x 92=0 11x(x 4) 23(x 4)=0 Solving we get x= ...

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Byju's Answer

Standard X

Mathematics

Fundamental Theorem of Arithmetic

Solve for x: ...

Question

Solve for x : $\frac{2}{x + 1} + \frac{3}{2 (x - 2)} = \frac{23}{5 x}$

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Solution

Given: $\frac{2}{x + 1} + \frac{3}{2 (x - 2)} = \frac{23}{5 x}$
$\frac{4 (x - 2) + 3 (x + 1)}{2 (x + 1) (x - 2)} = \frac{23}{5 x}$
$5 x (4 (x - 2) + 3 (x + 1)) = 46 (x + 1) (x - 2)$
$20 x (x - 2) + 15 x (x + 1) = 46 (x^{2} + x - 2 x - 2$
$20 x^{2} - 40 x + 15 x^{2} + 15 x = 46 (x^{2} - x - 2)$
$35 x^{2} - 25 x = 46 x^{2} - 46 x - 92$
$46 x^{2} - 35 x^{2} + 25 x - 46 x - 92 = 0$
$11 x^{2} - 21 x - 92 = 0$
$11 x^{2} - 44 x + 23 x - 92 = 0$
$11 x (x - 4) + 23 (x - 4) = 0$
$(x - 4) (11 x + 23) = 0$
Therefore, $x = (- \frac{23}{11})$ or 4

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