Question
Multiply the rational expression and write the product in the simplest form: (x^(2)+2x-3)/(x^(2)+3x-4)+(x^(2)+6x+8)/(x^(2)-9)
Answers
There are no human answers yet.
Answered by
GPT 3.5
To multiply the rational expression, we must first factorize the denominators:
Denominator 1: x^2 + 3x - 4 = (x + 4)(x - 1)
Denominator 2: x^2 - 9 = (x + 3)(x - 3)
Therefore, the expression becomes:
[(x^2 + 2x - 3)/(x + 4)(x - 1)] * [(x^2 + 6x + 8)/(x + 3)(x - 3)]
Next, we multiply the numerators and denominators:
[(x^2 + 2x - 3)(x^2 + 6x + 8)] / [(x + 4)(x - 1)(x + 3)(x - 3)]
Expanding the numerators:
[(x^4 + 8x^3 + 22x^2 + 16x - 24)] / [(x + 4)(x - 1)(x + 3)(x - 3)]
Simplifying the expression further is not possible in this case.
Denominator 1: x^2 + 3x - 4 = (x + 4)(x - 1)
Denominator 2: x^2 - 9 = (x + 3)(x - 3)
Therefore, the expression becomes:
[(x^2 + 2x - 3)/(x + 4)(x - 1)] * [(x^2 + 6x + 8)/(x + 3)(x - 3)]
Next, we multiply the numerators and denominators:
[(x^2 + 2x - 3)(x^2 + 6x + 8)] / [(x + 4)(x - 1)(x + 3)(x - 3)]
Expanding the numerators:
[(x^4 + 8x^3 + 22x^2 + 16x - 24)] / [(x + 4)(x - 1)(x + 3)(x - 3)]
Simplifying the expression further is not possible in this case.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.