[tex] \frac{4 {x}^{2} + 9 {y}^{2} }{4 {x}^{2} - 9 {y}^{2} } - \frac{3y}{2x + 3y} + \frac{3y}{3y - 2x} = \frac{4 {x}^{2} + 9 {y}^{2} }{(2x - 3y)(2x + 3y)} - \frac{3y}{2x + 3y} - \frac{3y}{2x - 3y} = \frac{4 {x}^{2} + 9 {y}^{2} - 3y(2x - 3y) - 3y(2x + 3y) }{(2x - 3y)(2x + 3y)} = \frac{4 {x}^{2} + 9 {y}^{2} - 6xy + 9 {y}^{2} - 6xy - 9 {y}^{2} }{(2x - 3y)(2x + 3y)} = \frac{4 {x}^{2} - 12xy + 9 {y}^{2} }{(2x - 3y)(2x + 3y)} = \frac{ {(2x - 3y)}^{2} }{(2x - 3y)(2x + 3y)} = \frac{2x - 3y}{2x + 3y} [/tex]
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[tex] \frac{4 {x}^{2} + 9 {y}^{2} }{4 {x}^{2} - 9 {y}^{2} } - \frac{3y}{2x + 3y} + \frac{3y}{3y - 2x} = \frac{4 {x}^{2} + 9 {y}^{2} }{(2x - 3y)(2x + 3y)} - \frac{3y}{2x + 3y} - \frac{3y}{2x - 3y} = \frac{4 {x}^{2} + 9 {y}^{2} - 3y(2x - 3y) - 3y(2x + 3y) }{(2x - 3y)(2x + 3y)} = \frac{4 {x}^{2} + 9 {y}^{2} - 6xy + 9 {y}^{2} - 6xy - 9 {y}^{2} }{(2x - 3y)(2x + 3y)} = \frac{4 {x}^{2} - 12xy + 9 {y}^{2} }{(2x - 3y)(2x + 3y)} = \frac{ {(2x - 3y)}^{2} }{(2x - 3y)(2x + 3y)} = \frac{2x - 3y}{2x + 3y} [/tex]