If 7x -15y = 4x + y , find the value of x : y. Hence, use componendo and dividendo to find the values of :

(i) $\frac{9 x + 5 y}{9 x - 5 y}$ (ii) $\frac{3 x^{2} + 2 y^{2}}{3 x^{2} - 2 y^{2}}$

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Solution

7x-15y=4x+y
7x-4x=y+15y
3x=16y
$left parenthesis i right parenthesisx over y equals 16 over 3m u l t i p l y i n g space b o t h space s i d e space b y space 9 over 5fraction numerator 9 x over denominator 5 y end fraction equals 144 over 15A p p l y i n g space c o m p o n e n d o space a n d space d i v d e n d ofraction numerator 9 x plus 5 y over denominator 9 x minus 5 y end fraction equals fraction numerator 144 plus 15 over denominator 144 minus 15 end fractionfraction numerator 9 x plus 5 y over denominator 9 x minus 5 y end fraction equals 159 over 129 equals 53 over 43left parenthesis i i right parenthesisx over y equals 16 over 3x squared over y squared equals 256 over 9m u l t i p l y i n g space b o t h space s i d e s space b y space 3 over 2fraction numerator 3 x squared over denominator 2 y squared end fraction equals 788 over 18 equals 128 over 3A p p l y i n g space c o m p o n e n d o space a n d space d i v i d e n d ofraction numerator 3 x squared plus 2 y squared over denominator 3 x squared minus 2 y squared end fraction equals fraction numerator 128 plus 3 over denominator 128 minus 3 end fractionfraction numerator 3 x squared plus 2 y squared over denominator 3 x squared minus 2 y squared end fraction equals 131 over 125A p p l y i n g space c o m p o n e n d o space a n d space d i v i d e n d o$

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