Question

Using synthetic division on 3x^3-4x^2+5/x-3/2 Would the answer be: 3x^2-x-3/2+26/4 / x-3/2

Answer 1

(3x^(3)-4x^(2)+5)/(x-(3)/(2))

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 2. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(3x^(3)-4x^(2)+5)/(x*(2)/(2)-(3)/(2))

Multiply x by 2 to get 2x.
(3x^(3)-4x^(2)+5)/((2x)/(2)-(3)/(2))

Combine the numerators of all expressions that have common denominators.
(3x^(3)-4x^(2)+5)/((2x-3)/(2))

Remove the parentheses around the (1)/(2).
(3x^(3)-4x^(2)+5)/(((1)/(2))(2x-3))

Multiply the factor by the rest of the expression to remove the fraction from the denominator. To divide by a factor, multiply by the reciprocal of the factor.
(3x^(3)-4x^(2)+5)/(2x-3)*2

Multiply the rational expressions to get (2(3x^(3)-4x^(2)+5))/((2x-3)).
(2(3x^(3)-4x^(2)+5))/(2x-3)