SOLUTION: (4x^2-10x+6)/(x^4-3x^3)devided by (2x-3)/(2x^3)*(x-3)/(2x-2)

Question 346796: (4x^2-10x+6)/(x^4-3x^3)devided by (2x-3)/(2x^3)*(x-3)/(2x-2)
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
((4x^(2)-10x+6)/(x^(4)-3x^(3))){(2x-3)/(2x^(3))*(x-3)/(2x-2)
Factor out the GCF of 2 from each term in the polynomial.
(((1)/(2x-3)*(2(2x^(2))+2(-5x)+2(3))/(x^(4)-3x^(3))))/(2x^(3))*(x-3)/(2x-2)
Factor out the GCF of 2 from 4x^(2)-10x+6.
(((1)/(2x-3)*(2(2x^(2)-5x+3))/(x^(4)-3x^(3))))/(2x^(3))*(x-3)/(2x-2)
In this problem -1*-(3)/(2)=3 and -1-(3)/(2)=-5, so insert -1 as the right hand term of one factor and -(3)/(2) as the right-hand term of the other factor.
(((1)/(2x-3)*(2(x-1)(x-(3)/(2)))/(x^(4)-3x^(3))))/(2x^(3))*(x-3)/(2x-2)
Remove the fraction by multiplying the first term of the factor by the denominator of the second term.
(((1)/(2x-3)*(2(x-1)(2x-3))/(x^(4)-3x^(3))))/(2x^(3))*(x-3)/(2x-2)
Factor out the GCF of x^(3) from each term in the polynomial.
(((1)/(2x-3)*(2(x-1)(2x-3))/(x^(3)(x)+x^(3)(-3))))/(2x^(3))*(x-3)/(2x-2)
Factor out the GCF of x^(3) from x^(4)-3x^(3).
(((1)/(2x-3)*(2(x-1)(2x-3))/(x^(3)(x-3))))/(2x^(3))*(x-3)/(2x-2)
Cancel the common factor of (2x-3) from the denominator of the first expression and the numerator of the second expression.
((1*(2(x-1))/(x^(3)(x-3))))/(2x^(3))*(x-3)/(2x-2)
Multiply the rational expressions to get (2(x-1))/(x^(3)(x-3)).
(((2(x-1))/(x^(3)(x-3))))/(2x^(3))*(x-3)/(2x-2)
Remove the parentheses around the 2x^(3) in the denominator.
(1)/(2x^(3))*(2(x-1))/(x^(3)(x-3))*(x-3)/(2x-2)
Cancel the common factor of 2 from the denominator of the first expression and the numerator of the second expression.
(1)/(x^(3))*(x-1)/(x^(3)(x-3))*(x-3)/(2x-2)
Multiply x^(3) by x^(3) to get x^(6).
(x-1)/((x^(6))(x-3))*(x-3)/(2x-2)
Remove the parentheses around the x^(6) in the denominator.
(x-1)/(x^(6)(x-3))*(x-3)/(2x-2)
Factor out the GCF of 2 from each term in the polynomial.
(x-1)/(x^(6)(x-3))*(x-3)/(2(x)+2(-1))
Factor out the GCF of 2 from 2x-2.
(x-1)/(x^(6)(x-3))*(x-3)/(2(x-1))
Cancel the common factor of (x-3) from the denominator of the first expression and the numerator of the second expression.
(x-1)/(x^(6))*(1)/(2(x-1))
Multiply x^(6) by 2 to get 2x^(6).
(x-1)/((2x^(6))(x-1))
Reduce the expression by canceling out the common factor of (x-1) from the numerator and denominator.
((x-1))/((2x^(6))(x-1))
Reduce the expression by canceling out the common factor of (x-1) from the numerator and denominator.
(1)/(2x^(6))
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