Math Help?

Question

I'm working on my math homework right now and ive done 6 out of 13 and im no too sure on how to do them if you could please answer these problems so i can check mine. Later I'll be posting my other 7 so stick around.

Perform indicated operation:

1.) ((7ab)/(9c)) * ((81c^2)/(91a^2b))

2.) ((x^2-y^2)/(a^2-b^2)) * ((a+b)/(x-y))

3.) ((a^2-ab)/(3a) divided by ((a-b)/(15b^2)

4.) ((x^2-2x+1)/(y-5)) divided by ((x-1)/(y^2-25)

5.) ((7)/(5a)-(10)/(3ab)

6.) ((6)/(x-5)+(7a))

Also, showing work and checks gets u best answer. And i really suck at math please help.

Answer 1

1.) 7ab/9c * 81c^2/91a^2b =
7*81abc^2 / 9*91a^2bc =
divide top and bottom by abc =
7*81c / 9*91a
Factor the numbers
7*9*9c / 9*7*13a
Eliminate the common factors (9*7)
= 9c/13a

2.) ((x^2-y^2)/(a^2-b^2)) * ((a+b)/(x-y)) =
((x^2 -y^2)(a+b)) / ((a^2-b^2)(x-y))
Factor the terms with squares
((x+y)(x-y)(a+b)) / ((a+b)(a-b)(x-y))
Eliminate the common terms (x-y)(a+b) from top and bottom
= (x+y)/(a-b)

3.) ((a^2-ab)/3a divided by ((a-b)/(15b^2))
Take the a out of first term leaves
(a-b)/3 divided by ((a-b))/(15b^2))
Flip the terms and multiply
((a-b)(15b^2)) / (3(a-b))
Divided top and bottom by 3(a-b)
= 5b^2

4.) ((x^2-2x+1)/(y-5)) divided by ((x-1)/(y^2-25))
Flip the terms and multiply
((x^2-2x+1)(y^2-25)) / ((y-5)(x-1))
Factor (x^2-2x+1) into (x-1)(x-1)
Factor (y^2-25) into (y+5)(y-5)
Divide top and bottom by (y-5)(x-1)
= (x-1)(y+5)

5.) 7/5a - 10/3ab
Common denominator is 15ab
7*3b/15ab - 10*5/15ab
= (21b - 50) / 15ab

6.) 6/(x-5) +7a
Common denominator is (x-5)
6/(x-5) +7a(x-5)/(x-5)
= (7ax - 35a - 6) / (x-5)

Answer 2

I think that you're being asked to simplify these equations.
for #1, for example, put all the numerators together and then all the denominators:
7ab*81c^2
over
9c*91a^b

Then "alphabetize" by combining like terms:
7*81abc^2
over
9*91a^2bc

Then factor the non-prime numbers and remove any terms that are in both the numerator and the denominator:
7*9*9*abc*c
over
9*91*abc*a

note the occurence of a 9 in both the numerator and denominator. On paper, you can cross these out. Also cross out the "abc" in both the numerator and denominator.

You should end up with 63c/91a

Try the rest; it's a similar process!

Answer 3

1) cancel out ab( the one beside the 7) with a^2b( beside 91),and divide 9c by 81c^2 which = 9c
the final answer for this one is 63c/91a

2) factor x^2 - y^2, you'll get (x-y)(x+y) , factor a^2-b^2 , you'll get (a-b)(a+b)
now cancel out (x-y) on the top with (x-y)on the bottom
cancel out (a+b)on the bottom with (a+b) on the top

so the final answer is (x+y)/(a-b)

3)for this one you have to flip the second part b/c it's a division problem , factor a out of a^2-ab ,then start to cancel out (a-b)with (a-b)......etc

the simplest answer for this problem is 5b^2

4)factor (x^2-2x+1) and (y^2-25)
then cancel out (x-1) on the top with (x-1)on the bottom,& (y-5) with (y-5)
until you get to the simplest form which is (x-1)(y+5)

5) take the least common denominator which is 15ab
you'll get (21b/15ab)-(50/15ab)
so, (21b-50)/15ab is the final answer

6)take the least common denominator which is x-5

so , (6/x-5)/(x-5) + (7ax-35a)/(x-5)
group them together : (7ax-35a+6)/(x-5)


good luck

Answer 4

1.) ((7ab)/(9c)) * ((81c^2)/(91a^2b))
=(7*81 abc^2)/(9*91 a^2bc)
=9c/13a

2.) ((x^2-y^2)/(a^2-b^2)) * ((a+b)/(x-y))
=((x^2-y^2)*(a+b))/((a^2-b^2)*(x-y))
=((x-y)*(x+y)*(a+b))/((a-b)*(a+b)*(x-y))
=(x+y)/(a-b)

3.) ((a^2-ab)/(3a) divided by ((a-b)/(15b^2)
=(a^2-ab)*(15b^2)/(3a)*(a-b)
=(15a^2b^2-15ab^3)/(3a^2-3ab)
=5b^2(3a^2-3ab)/(3a^2-3ab)
=5b^2

4.) ((x^2-2x+1)/(y-5)) divided by ((x-1)/(y^2-25)
=((x^2-2x+1)*(y^2-25))/((y-5)*(x-1))
=((x-1)*(x-1)*(y-5)(y+5))/((y-5)*(x-1))
=(x-1)*(x+5)

5.) ((7)/(5a)-(10)/(3ab)
=((7*3ab-10*5a)/(5a)*(3ab))
=(21ab-50b)/15a^2b
=b(21a-50)/15a^2b
=(21a-50)/15a^2

6.) ((6)/(x-5)+(7a))
=(6+7a*(x-5))/(x-5)
=(6-7ax-35a)/(x-5)

Answer 5

The only way you are going to get better at math is to do the work yourself. How do you know your math teacher isn't on here and won't see this? Now get off the internet and do your homework yourself because you can't post your test on the internet so others can do the work for you!