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((2x^(2)+11 x-9))/((2x-3))

2x2+11x−92x−3\frac{2x^{2}+11x-9}{2x-3}

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Full solution

Q. 2x2+11x−92x−3\frac{2x^{2}+11x-9}{2x-3}
  1. Identify expression to simplify: Identify the expression to simplify: ((2x2+11x−9)/(2x−3))((2x^2 + 11x - 9) / (2x - 3)).\newlineWe need to divide the polynomial 2x2+11x−92x^2 + 11x - 9 by the binomial 2x−32x - 3.
  2. Perform polynomial division: Perform polynomial division: Divide 2x22x^2 by 2x2x to get xx. Multiply xx by (2x−3)(2x - 3) to get 2x2−3x2x^2 - 3x. Subtract (2x2−3x)(2x^2 - 3x) from (2x2+11x−9)(2x^2 + 11x - 9) to get 14x−914x - 9.
  3. Continue the division: Continue the division: Divide 14x14x by 2x2x to get 77. Multiply 77 by (2x−3)(2x - 3) to get 14x−2114x - 21. Subtract (14x−21)(14x - 21) from (14x−9)(14x - 9) to get 1212.

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