Find the product and simplify 4y/(y^2-81) × (y+9)/2y^2

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Find the product and simplify 4y/(y^2-81) × (y+9)/2y^2

Mathematics
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2y3 y−9
Thats not one of the options ):
.....

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Other answers:

2y3/y-9?
Thats not one of the choices..
sorry :(
Thats ok.
wait @ashley9337 . I think I can do it
Okay thank you !!
Can you tag me when you figure it out? Thank you
oh! ok . sure :)
\[\frac{ 2 }{ y(y-9) }\]
Thank you so much!
np :)
@imqwerty can you explain it to me ?
ok :)
@imqwerty can you help me with 3 more problems?
\[\frac{ 4y }{ y^2-81 }\times \frac{ y+9 }{ 2y^2 }\] use the identity a^2 - b^2=(a+b)(a-b) in here - y^2 -81 u et-\[\frac{ 4y }{ (y+9)(y-9) }\times \frac{ y+9 }{2y^2}\]cut out the common things from numerator and denominator u get-\[\frac{ 2 }{ y(y-9) }\]
ok
What is the least commonn denominator for 3/x and 2/4xy
oh ! OK . Got it @imqwerty
least common divisor is the least common multiple. its 4xy
Oh okay i understand. There a harder one that i have no idea about, find the lcd for x^2/(x^2+4x+3) and 2x/ (x^2+x-6)
x^2+4x+3 --->(x+3)(x+1) x^2+x-6------>(x+3)(x-2) so the lcd wuld be (x+3)(x-2)(x+1)
Thank you for explaining it! okay can you help me with one last question
ok :)
Find the quotient and show all work please so i can understand how to do it :) x^2-6x/7 ÷ x-6/x
ok :)
\[\frac{ x^2-6x }{ 7}\div \frac{ (x-6) }{ x}\] we know that \[a \div b =a \times \frac{ 1 }{ b }\] so we get - \[\frac{ x^2-6x }{ 7 } \times \frac{ x }{ (x-6) }\] take x common from x^2-6x u get->x(x-6) \[\frac{ x(x-6) }{ 7 } \times \frac{ x }{ x-6 }\]\[\frac{ x^2 }{ 7 }\]
So the answer is x^2/7 right? Thank you so much for explaining it all.to me, i understand it now :)

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