(x^(2)-11x+30)/(x^(2)-25)*(x^(2)+6x+5)/(x-5x-6) simplify the rational expression
1 answer:
Simplify the following: ((x^2 - 11 x + 30) (x^2 + 6 x + 5))/((x^2 - 25) (x - 5 x - 6)) The factors of 5 that sum to 6 are 5 and 1. So, x^2 + 6 x + 5 = (x + 5) (x + 1): ((x + 5) (x + 1) (x^2 - 11 x + 30))/((x^2 - 25) (x - 5 x - 6)) The factors of 30 that sum to -11 are -5 and -6. So, x^2 - 11 x + 30 = (x - 5) (x - 6): ((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (x - 5 x - 6)) x - 5 x = -4 x: ((x - 5) (x - 6) (x + 5) (x + 1))/((x^2 - 25) (-4 x - 6)) Factor -2 out of -4 x - 6: ((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (2 x + 3) (x^2 - 25)) x^2 - 25 = x^2 - 5^2: ((x - 5) (x - 6) (x + 5) (x + 1))/(-2 (x^2 - 5^2) (2 x + 3)) Factor the difference of two squares. x^2 - 5^2 = (x - 5) (x + 5): ((x - 5) (x - 6) (x + 5) (x + 1))/(-2(x - 5) (x + 5) (2 x + 3)) ((x - 5) (x - 6) (x + 5) (x + 1))/((x - 5) (x + 5) (-2) (2 x + 3)) = ((x - 5) (x + 5))/((x - 5) (x + 5))×((x - 6) (x + 1))/(-2 (2 x + 3)) = ((x - 6) (x + 1))/(-2 (2 x + 3)): ((x - 6) (x + 1))/(-2 (2 x + 3)) Multiply numerator and denominator of ((x - 6) (x + 1))/(-2 (2 x + 3)) by -1:Answer: (-(x - 6) (x + 1))/(2 (2 x + 3))
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