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$begin mathsize 14px style limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared minus 6 x plus 7 end root plus square root of 4 x squared plus 3 x minus 7 end root minus square root of 25 x squared minus 5 x plus 7 end root close parentheses equals limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared minus 6 x plus 7 end root plus square root of 4 x squared plus 3 x minus 7 end root minus square root of 25 x squared minus 5 x plus 7 end root minus 3 x minus 2 x plus 5 x close parentheses equals limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared minus 6 x plus 7 end root plus square root of 4 x squared plus 3 x minus 7 end root minus square root of 25 x squared minus 5 x plus 7 end root minus square root of 9 x squared end root minus square root of 4 x squared end root plus square root of 25 x squared end root close parentheses equals limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared minus 6 x plus 7 end root minus square root of 9 x squared end root plus square root of 4 x squared plus 3 x minus 7 end root minus square root of 4 x squared end root plus square root of 25 x squared end root minus square root of 25 x squared minus 5 x plus 7 end root close parentheses equals limit as x rightwards arrow infinity of invisible function application open parentheses square root of 9 x squared minus 6 x plus 7 end root minus square root of 9 x squared end root close parentheses plus limit as x rightwards arrow infinity of invisible function application open parentheses square root of 4 x squared plus 3 x minus 7 end root minus square root of 4 x squared end root close parentheses plus limit as x rightwards arrow infinity of invisible function application open parentheses square root of 25 x squared end root minus square root of 25 x squared minus 5 x plus 7 end root close parentheses equals fraction numerator negative 6 minus 0 over denominator 2 square root of 9 end fraction plus fraction numerator 3 minus 0 over denominator 2 square root of 4 end fraction plus fraction numerator 0 minus open parentheses negative 5 close parentheses over denominator 2 square root of 25 end fraction equals fraction numerator negative 6 over denominator 2 times 3 end fraction plus fraction numerator 3 over denominator 2 times 2 end fraction plus fraction numerator 5 over denominator 2 times 5 end fraction equals fraction numerator negative 6 over denominator 6 end fraction plus 3 over 4 plus 5 over 10 equals negative 1 plus 3 over 4 plus 1 half equals fraction numerator negative 4 plus 3 plus 2 over denominator 4 end fraction equals 1 fourth end style$