Question

Multiplying and Dividing Rational Expressions?



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Answer 1

@whpalmer4

Answer 2

\[
3m-9 = 3(m-3)
\]Also \[
m^2-9 = (m+3)(m-3)
\]

Answer 3

\[
4m+8 = 4(m+2)
\]

Answer 4

So basically, I'm just factoring all of them.

Answer 5

Can you factor \(m^2+5m+6\)?

Answer 6

Do you have an idea of how to factor?

Answer 7

\[
(m+a)(m+b) = m^2+am + bm+ab = m^2+(a+b)m+ab
\]

Answer 8

Think about \(ab = 6\) and \(a+b=5\)

Answer 9

\(
(2)(3) = 6
\) and \(2+3=5\). This means \((m+2)(m+3) = m^2+5m+6\)

Answer 10

You will see that \((m+3)\) will cancel, so will \((m+2)\) and \((m-3)\).

Answer 11

\[
\frac{3(m-3)}{4(m+2)}\cdot \frac{(m+2)(m+3)}{(m-3)(m+3)} = \frac{3\color{red}{\cancel{(m-3)}}}{4\cancel{(m+2)}}\cdot \frac{\cancel{(m+2)}\color{blue}{\cancel{(m+3)}}}{\color{red}{\cancel{(m-3)}}\color{blue}{\cancel{(m+3)}}} = \frac{3}{4}
\]