Simplify -3a^2/a^2-4b^2 + 3a/a-2b?

Question

The answer's 6ab/a^2-4b^2 but how?

the other one is
slove the equation 6/5r-2 -1/4 = 3/4-10r

please explain!

Answer 1

-3a^2/(a^2-4b^2) + 3a/(a-2b)
-3a^2/{(a-2b)(a+2b)} +3a(a+2b)/[{(a-2b)(a+2b)]
= (-3a^2 +3a^2 +6ab)/(a^2-4b^2)
= 6ab/(a^2-b^2)

6/(5r-2) -1/4 = 3/(4-10r)
6/(5r-2) -.25(5r-2)/(5r-2) = -1.5/(5r-2)
5.75/(5r-2) = -1.5/(5r-2)
- 7.5 r +3 = 28.75 r - 11.5
25.75r = - 4
r = - .15534

Answer 2

Firstly think of these as regular fractions with different denominators. What would you do to add them together? The answer is find a common denominator. We can do this easily by factoring the denominators and then multiplying to get a common denominator.

[-3a^2] / [a^2 - 4b^2] + [3a] / [ a - 2b]
[-3a^2] / [(a - 2b)(a + 2b)] + [3a] / [ a - 2b]
~Our common denominator is (a - 2b)(a + 2b) because the 2nd fraction already has a (a-2b) in it.~
[-3a^2] / [(a - 2b)(a + 2b)] + [3a(a + 2b)] / [ a - 2b(a + 2b)]
[-3a^2] / [(a - 2b)(a + 2b)] + [3a*a + 3a*2b] / [ a - 2b(a + 2b)]
[-3a^2] / [(a - 2b)(a + 2b)] + [3a^2 + 6ab] / [ a - 2b(a + 2b)]
~add the two together~
[-3a^2 + 3a^2 + 6ab] / [ a - 2b(a + 2b)]
~so now we must simplify it!~
[-3a^2 + 3a^2 + 6ab] / [ a - 2b(a + 2b)]
~-3a^2 + 3a^2 = 0~
[6ab] / [ a - 2b(a + 2b)]
~we can use foil on the denominator and see if we can simplify it more after.~
[6ab] / [ a^2 - 4b^2]

And that should be as simple as you can get.

[6/5]r - 2 - [1/4] = [3/4] - 10r
~we can start by: -2 - [1/4] = - 8/4 - 1/4 = 8/4~
[6/5]r + [9/4] = [3/4] - 10r
~subtract 3/4~
[6/5]r + [9/4] - [3/4] = [3/4] - 10r - [3/4]
[6/5]r + [6/4] = -10r
~subtract [6/5]r~
[6/5]r + [6/4] - [6/5]r = -10r - [6/5]r
[6/4] = [56/5]r
[6/4] * [5/56]= [56/5]r * [5/56]
~same thing as dividing by [56/5]~
30/224 = r
~simplify the fraction~
15/112 = r
r = 15/112