|
Question 387946: y^2-5y/y^2+7y+12 divided by y^3-14y^2+45y/y^2+9y+18
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (y^(2)-(5y)/(y^(2))+7y+12)/(y^(3)-14y^(2)+(45y)/(y^(2))+9y+18)
Reduce the expression -(5y)/(y^(2)) by removing a factor of y from the numerator and denominator.
(y^(2)-(5)/(y)+7y+12)/(y^(3)-14y^(2)+(45y)/(y^(2))+9y+18)
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 y. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(y^(2)*(y)/(y)+7y*(y)/(y)-(5)/(y)+12*(y)/(y))/(y^(3)-14y^(2)+(45y)/(y^(2))+9y+18)
Complete the multiplication to produce a denominator of y in each expression.
((y^(3))/(y)+(7y^(2))/(y)-(5)/(y)+(12y)/(y))/(y^(3)-14y^(2)+(45y)/(y^(2))+9y+18)
Combine the numerators of all expressions that have common denominators.
((y^(3)+7y^(2)-5+12y)/(y))/(y^(3)-14y^(2)+(45y)/(y^(2))+9y+18)
Reorder the polynomial y^(3)+7y^(2)-5+12y alphabetically from left to right, starting with the highest order term.
((y^(3)+7y^(2)+12y-5)/(y))/(y^(3)-14y^(2)+(45y)/(y^(2))+9y+18)
Reduce the expression (45y)/(y^(2)) by removing a factor of y from the numerator and denominator.
((y^(3)+7y^(2)+12y-5)/(y))/(y^(3)-14y^(2)+(45)/(y)+9y+18)
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 y. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
((y^(3)+7y^(2)+12y-5)/(y))/(y^(3)*(y)/(y)-14y^(2)*(y)/(y)+9y*(y)/(y)+(45)/(y)+18*(y)/(y))
Complete the multiplication to produce a denominator of y in each expression.
((y^(3)+7y^(2)+12y-5)/(y))/((y^(4))/(y)-(14y^(3))/(y)+(9y^(2))/(y)+(45)/(y)+(18y)/(y))
Combine the numerators of all expressions that have common denominators.
((y^(3)+7y^(2)+12y-5)/(y))/((y^(4)-14y^(3)+9y^(2)+45+18y)/(y))
Reorder the polynomial y^(4)-14y^(3)+9y^(2)+45+18y alphabetically from left to right, starting with the highest order term.
((y^(3)+7y^(2)+12y-5)/(y))/((y^(4)-14y^(3)+9y^(2)+18y+45)/(y))
To divide by ((y^(4)-14y^(3)+9y^(2)+18y+45))/(y), multiply by the reciprocal of the fraction.
(y)/(y^(4)-14y^(3)+9y^(2)+18y+45)*(y^(3)+7y^(2)+12y-5)/(y)
Cancel the common factor of y from the numerator of the first expression and denominator of the second expression.
(1)/(y^(4)-14y^(3)+9y^(2)+18y+45)*(y^(3)+7y^(2)+12y-5)
Multiply the rational expressions to get ((y^(3)+7y^(2)+12y-5))/((y^(4)-14y^(3)+9y^(2)+18y+45)).
(y^(3)+7y^(2)+12y-5)/(y^(4)-14y^(3)+9y^(2)+18y+45)
|
|
|
| |
