SOLUTION: Please show me how to SOLVE my homework question. thanks. Y^2-36/y^2-4 multiplied by y^2+6y+8/y^2-2y-24 the choices are: A.) y+6/y-2 B.) y-6/y+2 c.) y+2/y+6 D.) y-2/y

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Question 77522: Please show me how to SOLVE my homework question. thanks.
Y^2-36/y^2-4 multiplied by y^2+6y+8/y^2-2y-24

the choices are:
A.) y+6/y-2 B.) y-6/y+2 c.) y+2/y+6 D.) y-2/y-6

Found 2 solutions by 303795, jim_thompson5910:
Answer by 303795(602)   (Show Source): You can put this solution on YOUR website!

Factorise each expression




Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Factor the first numerator
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to -36 and add to 0? Lets find out by listing all of the possible factors of -36


Factors:

1,2,3,4,6,9,12,18,36,

-1,-2,-3,-4,-6,-9,-12,-18,-36,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -36.

(-1)*(36)=-36

(-2)*(18)=-36

(-3)*(12)=-36

(-4)*(9)=-36

(-6)*(6)=-36

Now which of these pairs add to 0? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 0

||||||||||
First Number|Second Number|Sum
1|-36|1+(-36)=-35
2|-18|2+(-18)=-16
3|-12|3+(-12)=-9
4|-9|4+(-9)=-5
6|-6|6+(-6)=0
-1|36|(-1)+36=35
-2|18|(-2)+18=16
-3|12|(-3)+12=9
-4|9|(-4)+9=5
-6|6|(-6)+6=0
We can see from the table that -6 and 6 add to 0.So the two numbers that multiply to -36 and add to 0 are: -6 and 6 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=-6 and b=6 So the equation becomes: (x-6)(x+6) Notice that if we foil (x-6)(x+6) we get the quadratic again



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Factor the first denominator
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to -4 and add to 0? Lets find out by listing all of the possible factors of -4


Factors:

1,2,4,4,6,9,12,18,36,

-1,-2,-4,-4,-6,-9,-12,-18,-36,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -4.

(-1)*(36)=-4

(-2)*(18)=-4

(-4)*(12)=-4

(-4)*(9)=-4

(-6)*(6)=-4

Now which of these pairs add to 0? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 0

||||||||||
First Number|Second Number|Sum
1|-36|1+(-36)=-35
2|-18|2+(-18)=-16
4|-12|4+(-12)=-8
4|-9|4+(-9)=-5
6|-6|6+(-6)=0
-1|36|(-1)+36=35
-2|18|(-2)+18=16
-4|12|(-4)+12=8
-4|9|(-4)+9=5
-6|6|(-6)+6=0
We can see from the table that -6 and 6 add to 0.So the two numbers that multiply to -4 and add to 0 are: -6 and 6 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=-6 and b=6 So the equation becomes: (x-6)(x+6) Notice that if we foil (x-6)(x+6) we get the quadratic again



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Factor the second numerator
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to 8 and add to 6? Lets find out by listing all of the possible factors of 8


Factors:

1,2,4,8,6,9,12,18,36,

-1,-2,-4,-8,-6,-9,-12,-18,-36,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 8.

1*36=8

2*18=8

4*12=8

8*9=8

6*6=8

(-1)*(-36)=8

(-2)*(-18)=8

(-4)*(-12)=8

(-8)*(-9)=8

(-6)*(-6)=8

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 6

||||||||||
First Number|Second Number|Sum
1|36|1+36=37
2|18|2+18=20
4|12|4+12=16
8|9|8+9=17
6|6|6+6=12
-1|-36|-1+(-36)=-37
-2|-18|-2+(-18)=-20
-4|-12|-4+(-12)=-16
-8|-9|-8+(-9)=-17
-6|-6|-6+(-6)=-12
substitute a=-6 and b=6 So the equation becomes: (x-6)(x+6) Notice that if we foil (x-6)(x+6) we get the quadratic again None of these factors add to 6. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.


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Factor the second denominator
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to -24 and add to -2? Lets find out by listing all of the possible factors of -24


Factors:

1,2,3,4,6,8,12,24,36,

-1,-2,-3,-4,-6,-8,-12,-24,-36,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -24.

(-1)*(36)=-24

(-2)*(24)=-24

(-3)*(12)=-24

(-4)*(8)=-24

(-6)*(6)=-24

Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

||||||||||
First Number|Second Number|Sum
1|-36|1+(-36)=-35
2|-24|2+(-24)=-22
3|-12|3+(-12)=-9
4|-8|4+(-8)=-4
6|-6|6+(-6)=0
-1|36|(-1)+36=35
-2|24|(-2)+24=22
-3|12|(-3)+12=9
-4|8|(-4)+8=4
-6|6|(-6)+6=0
substitute a=-6 and b=6 So the equation becomes: (x-6)(x+6) Notice that if we foil (x-6)(x+6) we get the quadratic again None of these factors add to -2. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.






So the whole expression becomes




Cancel like terms
So the whole expression reduces to

So the answer is A)
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