[(w/6)-(6/w)]/[(6/w-4)+(w/2)]

Question

This isn't a word problem but I am struggling. Merry Christmas, by the way!~~

Answer 1

Remember that when you add /subtract fractions you need to have the same denominator. Let's start with the top part of the fraction and simplify it:

(w/6)-(6/w) The easiest way to get a common denominator is to multiply the numerator and denominator of the first fraction, w/6, by the denominator of the second fraction, w, and multiply the numerator and denominator of the second fraction, 6/w, by the denominator of the first fraction and the new common denominator will be 6w:

(w/6)(w/w)-(6/w)(6/6)

(w²/6w)-(36/6w)--->(w²-36)/6w

Do the same for the bottom part of our fraction, [(6/w-4)+(w/2)].

(6/w)-4=(6-4w)/w--->(6-4w)/(w)+(w/2)--->(12-8w+w²)/2w

[(w²-36)/(6w)]/[(w²-8w+12)/(2w)]

Dividing by a fraction is the same as multiplying by its' reciprocal, so we get:

[(w²-36)/(6w)][(2w)/(w²-8w+12)]. Rearranging this we get:

[(w²-36)/(w²-8w+12)][(2w)/(6w)]

[(w-6)(w+6)/(w-6)(w-2)](1/3) factoring and simplifying

(w+6)/3(w-2)--->(w+6)/(3w-6) The answer!

I know this is a lot, but just remember that you need to get the denominators the same before you can add and/or subtract them. I hope this helps!

Merry Christmas to you, too!