Question

$\frac{4}{x} - 3 = \frac{5}{2x + 3}$
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Answer 1

Answer:

$x = - 2 \: \: \: \: or \: \: \: \: x = 1$

Step-by-step explanation:

$\frac{4}{x} - 3 = \frac{5}{2x + 3} \\ = > \frac{4 - 3x}{x} = \frac{5}{2x + 3} \\ = > (4 - 3x)(2x + 3) = 5x \\ = > 8x + 12 - 6 {x}^{2} - 9x = 5x \\ = > 12 - 6 {x}^{2} + 8x - 9x - 5x = 0 \\ = > - 6 {x}^{2} - 6x + 12 = 0 \\ = > - 6 {x}^{2} - 12x + 6x + 12 = 0 \\ = > - 6x(x + 2) + 6(x + 2) = 0 \\ = > (x + 2)( - 6x + 6) = 0 \\ = > (x + 2) = 0 \: \: \: or \: ( - 6x + 6) = 0 \\ = > x = - 2 \: or \: x = 1$

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