Question

Can someone please explain the process behind simplifying this please:

24 y^6 z^7 + 18 y^5 Z^6
----------------------
6 z^3 y^4

Answer 1

any ideas on the common factor for the numerator?

Answer 2

so: 6 y^5 z^6 (4 y z + 3) as the numerator?

Answer 3

sorry the site is a bit lagged... yes

Answer 4

(it's ok, thank you!) after eliminating would y^2 z^2 (4 y z + 3) be next?

Answer 5

\(\bf \cfrac{24 y^6 z^7 + 18 y^5 z^6 }{6 z^3 y^4}\implies \cfrac{6y^5z^6(4yz+3)}{6 z^3 y^4}\implies \cfrac{\cancel{ 6 }\cancel{ y^4 }y\cancel{ z^3 }z^3(4yz+3)}{\cancel{ 6 }\cancel{ z^3 }\cancel{ y^4 }}\)

Answer 6

and that's all you could simplify it to

Answer 7

That makes sense but the question was part of a a multiple choice thing & that wasn't an option.

Answer 8

hmmmm so.. what choices were you given?

Answer 9

(I substituted x with z so it wouldn't be confusing)

Answer 10

I most likely foiled it incorrectly...

Answer 11

hmm

Answer 12

ohh I see the issue, there's no "z" variables there

Answer 13

I substituted the X with the Z so it wouldn't be confusing, it's the same otherwise.

Answer 14

wooop.... sorry was caught up a bit so

Answer 15

\(\bf \cfrac{24 y^6 x^7 + 18 y^5 x^6 }{6 x^3 y^4}\implies \cfrac{6y^5x^6(4yx+3)}{6 x^3 y^4}\implies \cfrac{\cancel{ 6 }\cancel{ y^4 }y\cancel{ x^3 }x^3(4yx+3)}{\cancel{ 6 }\cancel{ x^3 }\cancel{ y^4 }}
\\ \quad \\
yx^3(4yx+3)\implies 4y^2x^4+3yx^3\implies 3x^3y+4x^4y^2\)

Answer 16

Thank you!!!