# help in determining common denom. for ratl. expressions

#### dk_102

##### New member
-4/3w+9 + 6/4w+12

Question is simplify/state restrictions

- my question is how would you determine the common denominator?

appreciate any help

dom

#### jonboy

##### Full Member
Do you mean: $$\displaystyle \L -\;\frac{4}{3w+9} \,+\, \frac{6}{4w+12} \;or\; -\,\frac{4}{3}w \,+ \,9 \frac{6}{4}w \,+\, 12 \;or \; -\,\frac{4}{3w} \,+ \,9 \frac{6}{4w} \,+\, 12$$?? Or something else?

#### skeeter

##### Senior Member
I assume you mean the expression

$$\displaystyle \L \frac{-4}{3w+9} + \frac{6}{4w+12}$$

factor the denominators to see what they have in common ...

$$\displaystyle \L \frac{-4}{3(w+3)} + \frac{6}{4(w+3)}$$

note that the denominators have the factors (w+3), 4, and 3 ... so, the common denominator will be (w+3)(4)(3) = 12(w+3).

$$\displaystyle \L \frac{(-4)(4)}{(4)(3)(w+3)} + \frac{(6)(3)}{(4)(3)(w+3)}$$

$$\displaystyle \L \frac{-16}{12(w+3)} + \frac{18}{12(w+3)}$$

can you finish up now?

#### dk_102

##### New member
thank you

ya thanks skeeter that helps alot wasn't thinking thanks a bunch...

dom