Question

Solve 7y-2/5y-1=7y+3/5y+4​

Answer 1

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$7y - \frac{2}{5y - 1} = 7y + \frac{3}{5y + 4} \\ \frac{7y \times (5y - 1 ) - 2}{5y - 1} = \frac{7y \times (5y + 4) + 3}{5y + 4}$

$\frac{35 {y}^{2} - 7y - 2 }{5y - 1} = \frac{35 {y}^{2} + 28y + 3}{5y + 4} \\ (5y + 4)(35 {y}^{2} - 7y - 2) = (5y - 1)(35 {y}^{2} + 28y + 3) \\ 175 {y}^{3} - 35 {y}^{2} - 10y + 140 {y}^{2} - 28y - 8 = 175 {y}^{3} + 140 {y}^{2} + 15y - 35 {y }^{2} - 28y - 3 \\ 175 {y}^{3} - 175 {y}^{3} - 35 {y}^{2} + 35 {y}^{2} + 140 {y}^{2} - 140 {y}^{2} - 38y - 8 = - 13y - 3 \\ - 38y - 8 = - 13y - 3 \\ 38y - 13y = - 8 + 3 \\ 25y = - 5 \\ y = - \frac{5}{25}$

$y = - \frac{1}{5}$

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