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Question 388553: 2/y+4 divide 3/y-4-y^2-16
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! Please state your equation more clearly next time.
Which is didvided by which? I will do both this one time...next time put "divided by" or write it out as it appears.
((2)/(y)+4){((3)/(y)-4-y^(2)-16)
Divide the expression.
((2)/(y)+4)/((3)/(y)-4-y^(2)-16)
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.
((2)/(y)+4*(y)/(y))/((3)/(y)-4-y^(2)-16)
Complete the multiplication to produce a denominator of y in each expression.
((2)/(y)+(4y)/(y))/((3)/(y)-4-y^(2)-16)
Combine the numerators of all expressions that have common denominators.
((2+4y)/(y))/((3)/(y)-4-y^(2)-16)
Reorder the polynomial 2+4y alphabetically from left to right, starting with the highest order term.
((4y+2)/(y))/((3)/(y)-4-y^(2)-16)
Subtract 16 from -4 to get -20.
((4y+2)/(y))/((3)/(y)-20-y^(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 y. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
((4y+2)/(y))/(-y^(2)*(y)/(y)+(3)/(y)-20*(y)/(y))
Complete the multiplication to produce a denominator of y in each expression.
((4y+2)/(y))/(-(y^(3))/(y)+(3)/(y)-(20y)/(y))
Combine the numerators of all expressions that have common denominators.
((4y+2)/(y))/((-y^(3)+3-20y)/(y))
Reorder the polynomial -y^(3)+3-20y alphabetically from left to right, starting with the highest order term.
((4y+2)/(y))/((-y^(3)-20y+3)/(y))
Factor out the GCF of 2 from each term in the polynomial.
(((2(2y)+2(1))/(y)))/((-y^(3)-20y+3)/(y))
Factor out the GCF of 2 from 4y+2.
(((2(2y+1))/(y)))/((-y^(3)-20y+3)/(y))
To divide by ((-y^(3)-20y+3))/(y), multiply by the reciprocal of the fraction.
(y)/(-y^(3)-20y+3)*(2(2y+1))/(y)
Cancel the common factor of y from the numerator of the first expression and denominator of the second expression.
(1)/(-y^(3)-20y+3)*2(2y+1)
Multiply the rational expressions to get (2(2y+1))/((-y^(3)-20y+3)).
(2(2y+1))/(-y^(3)-20y+3)
NEXT EQUATION (FLIPPED)
(3)/(y)-4-y^(2)-16{(2)/(y)+4
Reduce the expression (16)/(2) by removing a factor of 2 from the numerator and denominator.
(3)/(y)-4-y^(2)-(8)/(y)+4
Combine the numerators of all expressions that have common denominators.
(3-8)/(y)-4-y^(2)+4
Subtract 8 from 3 to get -5.
(-5)/(y)-4-y^(2)+4
Move the minus sign from the numerator to the front of the expression.
-(5)/(y)-4-y^(2)+4
Add 4 to -4 to get 0.
-(5)/(y)-y^(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 y. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(5)/(y)-y^(2)*(y)/(y)
Complete the multiplication to produce a denominator of y in each expression.
-(5)/(y)-(y^(3))/(y)
Combine the numerators of all expressions that have common denominators.
(-5-y^(3))/(y)
Reorder the polynomial -5-y^(3) alphabetically from left to right, starting with the highest order term.
(-y^(3)-5)/(y)
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