Asked by Ian
Find the value of x that makes the following expression equal to zero: x^2+5x+6/x-1 divided by x+2/x^2-3x+2.
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the expression as [(x^2+5x+6)/(x-1)] ÷ [(x+2)/(x^2-3x+2)].
Rewrite as a product:
(x^2+5x+6)/(x-1) * (x^2-3x+2)/(x+2).
Factor:
(x+2)(x+3)/(x-1) * (x-1)(x-2)/(x+2) = (x+3)(x-2).
Set equal to zero:
(x+3)(x-2)=0 → x = -3 or x = 2.
Check domain restrictions: the original expression is undefined at x = 1, 2, and -2 (they make denominators or the divisor zero). Thus x = 2 and x = -2 are not allowed.
Therefore the only valid solution is x = -3.
Rewrite as a product:
(x^2+5x+6)/(x-1) * (x^2-3x+2)/(x+2).
Factor:
(x+2)(x+3)/(x-1) * (x-1)(x-2)/(x+2) = (x+3)(x-2).
Set equal to zero:
(x+3)(x-2)=0 → x = -3 or x = 2.
Check domain restrictions: the original expression is undefined at x = 1, 2, and -2 (they make denominators or the divisor zero). Thus x = 2 and x = -2 are not allowed.
Therefore the only valid solution is x = -3.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.