3x+1÷15x²+8x-12 Long division
And solutions
Answer (1)
Long division noteBecause the degree of the numerator (1) is less than the degree of the denominator (2), the polynomial long division gives:Quotient = 0, Remainder = 3x + 1.So as a rational expression: (3x + 1) ÷ (15x² + 8x − 12) = (3x + 1)/(15x² + 8x − 12) and it is already a proper rational function.Factor the denominator (useful for simplification or partial fractions)15x² + 8x − 12 = (5x + 6)(3x − 2).Check simplification3x + 1 does not share a factor with (5x + 6) or (3x − 2), so the fraction cannot be reduced.Write(3x + 1)/((5x + 6)(3x − 2)) = A/(5x + 6) + B/(3x − 2).Solving for A and B gives A = 13/28 and B = 9/28.Thus(3x + 1)/(15x² + 8x − 12) = 13/[28(5x + 6)] + 9/[28(3x − 2)].
