Question

What is the simplified form of the quantity (15xy^2/x^2+5x+6)/(5x^2y/2x^2+7x+3) ?

Answer 1

I believe it's the one I bubbled but I'm not sure

Answer 2

The expression can be rewritten by inverting the denominator to give:
\[\large \frac{15xy ^{2}}{x ^{2}+5x+6} \times \frac{2x ^{2}+7x+3}{5x ^{2}y}\]
Do you understand this step?

Answer 3

Yes I have that written down;
I converted x^2 + 5x + 6 into (x + 2)(x + 3)
And I also converted the 2x^2 + 7x + 3 into (2x + 1)(x + 3)
\[\frac{ 15y }{ (x + 2)(x + 3)} \times \frac{ (2x + 1)(x + 3) }{ 5x }\]

Answer 4

I cancelled out the exponents on 15xy^2 and 5x^2y

Answer 5

Am I supposed to do that?

Answer 6

You are correct so far. Now you can cancel (x + 3) in the denominator of the first term and in the numerator of the second term. Then divide 5x by 5 and divide 15y by 5.

Answer 7

Is that because the GCF of both 5x and 15y is 5?

Answer 8

Correct.

Answer 9

\[\frac{ 3y }{ (x + 2) }\times \frac{ (2x + 1) }{ x }\]
Like this?

Answer 10

Good work! So basically you have finished. Which answer option have you got?

Answer 11

\[\frac{ 3y(2x + 1) }{ x(x + 2) }\]

Oh okay so I did get it right. Thanks!

Answer 12

You're welcome :)