Question
Divide. (1 point) ((x^2 +2x+1/x^2 -8x+16)/ (x+1/x^2-16)
Answers
GPT 3.5
((x^2 + 2x + 1) / (x^2 - 8x + 16)) / ((x + 1) / (x^2 - 16))
= [(x + 1)^2 / (x - 4)^2] / [(x + 1) / (x^2 - 16)]
= [(x + 1)^2 / (x - 4)^2] * [(x^2 - 16) / (x + 1)]
= [(x + 1)(x + 1)(x - 4)(x + 4)] / [(x - 4)(x - 4)(x + 1)]
= (x + 1)(x + 4) / (x - 4)
= [(x + 1)^2 / (x - 4)^2] / [(x + 1) / (x^2 - 16)]
= [(x + 1)^2 / (x - 4)^2] * [(x^2 - 16) / (x + 1)]
= [(x + 1)(x + 1)(x - 4)(x + 4)] / [(x - 4)(x - 4)(x + 1)]
= (x + 1)(x + 4) / (x - 4)