Question
Simplify. state the result in simplest form. (2x+10)/(X^(2)+X-2)+(2)/(X+2)+(X)/(X-1),X!=-2,1
Answers
Answered by
GPT 3.5
(2x + 10)/(x^2 + x - 2) + 2/(x + 2) + x/(x - 1)
= (2x + 10)/(x^2 + x - 2) + 2/(x + 2) + x^2/(x^2 - x)
= (2x + 10)/((x + 2)(x - 1)) + 2/(x + 2) + x^2/(x(x - 1))
= (2x + 10 + 2(x - 1) + x^2)/(x(x + 2)(x - 1))
= (2x + 10 + 2x - 2 + x^2)/(x(x + 2)(x - 1))
= (3x + 8 + x^2)/(x(x + 2)(x - 1))
Therefore, the simplified form is (3x + 8 + x^2)/(x(x + 2)(x - 1)).
= (2x + 10)/(x^2 + x - 2) + 2/(x + 2) + x^2/(x^2 - x)
= (2x + 10)/((x + 2)(x - 1)) + 2/(x + 2) + x^2/(x(x - 1))
= (2x + 10 + 2(x - 1) + x^2)/(x(x + 2)(x - 1))
= (2x + 10 + 2x - 2 + x^2)/(x(x + 2)(x - 1))
= (3x + 8 + x^2)/(x(x + 2)(x - 1))
Therefore, the simplified form is (3x + 8 + x^2)/(x(x + 2)(x - 1)).