Question

lf x/y = 2/3 then 2x²+3y²/2x²- 3y²=?​

Answer 1

Final Answer: -35/9

Simplified steps:

Given,

$\frac{x}{y} = \frac{2}{3} \\ = > \: x = \frac{2}{3} y \: \: \: \: \: \: \: \: \: ...(1)$

Now,

$\frac{2{x}^{2} + 3 {y}^{2} }{2 {x}^{2} - 3 {y}^{2} }$

$= \frac{2({ \frac{2y}{3} })^{2} + 3 {y}^{2} }{2 ({ \frac{2y}{3} })^{2} - 3 {y}^{2} } = \frac{ \frac{8 {y}^{2} }{9} + 3 {y}^{2} }{\frac{8 {y}^{2} }{9} - 3 {y}^{2}}$

[by (1)]

$= \frac{8 {y}^{2} + 27 {y}^{2} }{9} \div \frac{8 {y}^{2} - 27 {y}^{2} }{9} \\ = \frac{35 {y}^{2} }{9} \times \frac{9}{ - 19 {y}^{2} } \: \: \: \: \: \: = - \frac{35}{19}$

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