SOLUTION: perform indicated operation: y^2+3y-4/y^2+7y+12 multiplied by 4y^2-36/4y^2-4

Question 389487: perform indicated operation:
y^2+3y-4/y^2+7y+12 multiplied by 4y^2-36/4y^2-4
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
(y^(2)+3y-4)/(y^(2)+7y+12)*(4y^(2)-36)/(4y^(2)-4)
In this problem 4*-1=-4 and 4-1=3, so insert 4 as the right hand term of one factor and -1 as the right-hand term of the other factor.
((y+4)(y-1))/(y^(2)+7y+12)*(4y^(2)-36)/(4y^(2)-4)
In this problem 4*3=12 and 4+3=7, so insert 4 as the right hand term of one factor and 3 as the right-hand term of the other factor.
((y+4)(y-1))/((y+4)(y+3))*(4y^(2)-36)/(4y^(2)-4)
Reduce the expression by canceling out the common factor of (y+4) from the numerator and denominator.
((y+4)(y-1))/((y+4)(y+3))*(4y^(2)-36)/(4y^(2)-4)
Reduce the expression by canceling out the common factor of (y+4) from the numerator and denominator.
(y-1)/(y+3)*(4y^(2)-36)/(4y^(2)-4)
Factor out the GCF of 4 from each term in the polynomial.
(y-1)/(y+3)*(4(y^(2))+4(-9))/(4y^(2)-4)
Factor out the GCF of 4 from 4y^(2)-36.
(y-1)/(y+3)*(4(y^(2)-9))/(4y^(2)-4)
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(y-1)/(y+3)*(4(y-3)(y+3))/(4y^(2)-4)
Factor out the GCF of 4 from each term in the polynomial.
(y-1)/(y+3)*(4(y-3)(y+3))/(4(y^(2))+4(-1))
Factor out the GCF of 4 from 4y^(2)-4.
(y-1)/(y+3)*(4(y-3)(y+3))/(4(y^(2)-1))
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(y-1)/(y+3)*(4(y-3)(y+3))/(4(y-1)(y+1))
Reduce the expression (4(y-3)(y+3))/(4(y-1)(y+1)) by removing a factor of 4 from the numerator and denominator.
(y-1)/(y+3)*((y-3)(y+3))/((y-1)(y+1))
Cancel the common factor of (y+3) from the denominator of the first expression and the numerator of the second expression.
(y-1)*(y-3)/((y-1)(y+1))
Reduce the expression by canceling out the common factor of (y-1) from the numerator and denominator.
(y-3))/(y+1)
Reduce the expression by canceling out the common factor of (y-1) from the numerator and denominator.
(y-3)/(y+1)
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