How do you combine #2/(5w+10) - 3/(2w-4)#?

We get

simplifying we get the result above.

To combine the expressions 2/(5w+10) and -3/(2w-4), we need to find a common denominator. The common denominator for these two expressions is (5w+10)(2w-4).

To get the first fraction with the common denominator, we multiply the numerator and denominator by (2w-4):

2/(5w+10) * (2w-4)/(2w-4) = 4w-8 / (10w+20)

For the second fraction, we multiply the numerator and denominator by (5w+10):

-3/(2w-4) * (5w+10)/(5w+10) = -15w-30 / (10w-20)

Now that both fractions have the same denominator, we can combine them:

(4w-8) / (10w+20) - (15w+30) / (10w-20)

To subtract the fractions, we need to find a common denominator again, which is (10w+20)(10w-20):

[(4w-8)(10w-20) - (15w+30)(10w+20)] / [(10w+20)(10w-20)]

Expanding and simplifying the numerator:

(40w^2 - 80w - 80w + 160 - 150w - 300) / [(10w+20)(10w-20)]

Combining like terms:

(40w^2 - 305w - 140) / [(10w+20)(10w-20)]

Therefore, the combined expression is (40w^2 - 305w - 140) / [(10w+20)(10w-20)].