Mathematics, 10.11.2020 21:40 hernandez09297
Jack wrote this solution to solve for x. Which statement is true? −3 is an extraneous solution because it is negative. 6 is an extraneous solution because it creates a zero in the denominator. There are no extraneous solutions. Both −3 and 6 are extraneous solutions because they create a 0 in the denominator. First line. Fraction numerator 1 over denominator x minus 5 end fraction equals fraction numerator x plus 3 end numerator over denominator x minus 6 end fraction minus fraction numerator 9 over denominator x squared minus 11 x plus 30 end fraction. Second line. Factor the expression. Fraction numerator 1 over denominator x minus 5 end fraction equals fraction numerator x plus 3 end numerator over denominator x minus 6 end fraction minus fraction numerator 9 over denominator left parenthesis x minus 6 right parenthesis left parenthesis x minus 5 right parenthesis end fraction. Third line. Multiply expression by the LCD. Factorize the expression. Fraction numerator 1 over denominator x minus 5 end fraction times left parenthesis x minus 6 right parenthesis left parenthesis x minus 5 right parenthesis equals fraction numerator x plus 3 end numerator over denominator x minus 6 end fraction times left parenthesis x minus 6 right parenthesis left parenthesis x minus 5 right parenthesis minus fraction numerator 9 over denominator left parenthesis x minus 6 right parenthesis left parenthesis x minus 5 right parenthesis end fraction times left parenthesis x minus 6 right parenthesis left parenthesis x minus 5 right parenthesis. Fourth line. Simplify the expression. x minus 6 equals left parenthesis x plus 3 right parenthesis left parenthesis x minus 5 right parenthesis minus 9. Fifth line. Simplify the expression. x minus 6 equals x squared minus 5 x plus 3 x minus 15 minus 9. Sixth line. Combine the like terms. 0 equals x squared minus 3 x minus 18. Seventh line. Use the zero product property. 0 equals left parenthesis x minus 6 right parenthesis left parenthesis x plus 3 right parenthesis. Eighth line. Solve these for the value of x. x equals 6 or x equals negative 3.
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Jack wrote this solution to solve for x. Which statement is true? −3 is an extraneous solution becau...
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