Question

solve 30/x-30/y=3 15/x-30/y=-3/2
the previous answer i got wan not clear​

Answer 1

$\frac{30}{x} - \frac{30}{y} = 3 \\ \\ \frac{30y - 30x}{xy} = 3 \\ \\ by \: cross \: multiplication \\ \\ 30y - 30x = 3xy \: \: \: \\ divide \: both \: side \: by \: 3 \\ \\ 10y - 10x = xy \: \: \: \: \: \: \: (1) \\ \\ \\ \frac{15}{x} - \frac{30}{y} = \frac{ - 3}{2} \\ \\ \frac{15y - 30x}{xy} = \frac{ - 3}{2 } \\ \\ by \: cross \: multiplication \\ \\ 30y - 60x = - 3xy \\ \\ divide \: both \: side \: by \: - 3 \\ \\ - 10y - 20x = xy \: \: \: \: \: \: \: \: (2) \\ \\ on \: comparing \: (1) \: and \: (2) \: we \: get \\ \\ 10y - 10x = - 10y - 20x \\ \\ 10y + 10y = - 20x + 10x \\ \\ 20y = - 10x \\ \\ y = \frac{ - 10x}{20} \\ \\ y = \frac{ - 1}{2} x \: \: \: (3) \\ \\ put \: y \: value \: in \: (1) \\ \\ 10y - 10x = xy \\ \\ 10( \frac{ - 1x}{2} ) - 10x = x( \frac{ - 1x}{2} ) \\ \\ - 5x - 10x = - \frac{ { x }^{2} }{2} \\ \\ - 15x = \frac{ - { x}^{2} }{2} \\ \\ by \: cross \: multiplying \\ \\ - 30x = - { x}^{2} \\ \\ 30= \frac{ { x}^{2} }{ x} \\ \\ x = 30 \\ \\ put \: x \: value \: in \: (3) \\ \\ y = \frac{ - 1x}{2} \\ \\ y = \frac{ - 1 \times 30}{2} \\ \\ y = \frac{ - 30}{2} \\ \\ y = - 15$

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