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Asked by Kanwaranita10 | 3rd Mar, 2020, 02:45: PM

Expert Answer:

To find x:y when (x2 + 2x)/2x+4=(y2 + 3y)/3y+9
fraction numerator x squared plus 2 x over denominator 2 x plus 4 end fraction equals fraction numerator y squared plus 3 y over denominator 3 y plus 9 end fraction
U sin 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
rightwards double arrow fraction numerator x squared plus 2 x plus 2 x plus 4 over denominator x squared plus 2 x minus 2 x minus 4 end fraction equals fraction numerator y squared plus 3 y plus 3 y plus 9 over denominator y squared plus 3 y minus 3 y minus 9 end fraction
rightwards double arrow fraction numerator x squared plus 4 x plus 4 over denominator x squared minus 4 end fraction equals fraction numerator y squared plus 6 y plus 9 over denominator y squared minus 9 end fraction
rightwards double arrow fraction numerator open parentheses x plus 2 close parentheses squared over denominator open parentheses x plus 2 close parentheses open parentheses x minus 2 close parentheses end fraction equals fraction numerator open parentheses y plus 3 close parentheses squared over denominator open parentheses y minus 3 close parentheses open parentheses y plus 3 close parentheses end fraction
rightwards double arrow fraction numerator open parentheses x plus 2 close parentheses over denominator open parentheses x minus 2 close parentheses end fraction equals fraction numerator open parentheses y plus 3 close parentheses over denominator open parentheses y minus 3 close parentheses end fraction
A g a i n space u sin 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 comma space w e space h a v e
rightwards double arrow fraction numerator x plus 2 plus x minus 2 over denominator x plus 2 minus x plus 2 end fraction equals fraction numerator y plus 3 plus y minus 3 over denominator y plus 3 minus y plus 3 end fraction
rightwards double arrow fraction numerator 2 x over denominator 4 end fraction equals fraction numerator 2 y over denominator 6 end fraction
rightwards double arrow x over y equals 4 over 6 equals 2 over 3
rightwards double arrow x colon y equals 2 colon 3

Answered by Renu Varma | 3rd Mar, 2020, 04:47: PM