if a/b=3/5 then 3a+2b/3a-2b?

Answer 1

a/b=3/5 does not require a=3 and b=5
(a,b)=[(3,5), (6,10), 9,15), ... etc )

Use a=(3/5)b

then 3a+2b/3a-2b=
(9/5)b + 2b/(9/5)b) - 2b=
-b/5 + 10/9

Did you mean (3a+2b)/(3a-2b) ? Then we have
((3/5)b + 2b)/( (3/5)b - 2b) =
[(13/5)b]/[-(7/5)b]=

-13/7

Answer 2

All we can do is work backwards from the original solution.

Note that both a and b must be nonzero, otherwise a/b would not equal 3/5.

First, let's see what (3a+2b)/(3a-2b) will give us.

Our first step would be to multiply the top and bottom by 1/b. This is completely a valid step because b is nonzero.

[(3a+2b)/b] / [(3a - 2b)/b]

Now, we can put them individually over b.

{ [3a/b] + [2b/b] } / { [3a/b] - [2b/b] }

[2b/b] will become 2, since the b will cancel out.

{ [3a/b] + 2 } / { [3a/b] - 2 }

Now, we will express [3a/b] as 3[a/b]

{ 3[a/b] + 2 } / { 3[a/b] - 2 }

Since it was given that a/b = 3/5, we just replace each instance of a/b with that, giving us

{ 3[3/5] + 2 } / {3 [3/5] - 2 }

And then we solve as normal.

{ [9/5] + 2 } / { [9/5] - 2 }

To get rid of the complex fraction (fractions within fractions), we multiply the top and bottom by 5, eliminating all denominators.

{ 9 + 2(5) } / { 9 - 2(5) }
{ 9 + 10 } / {9 - 10}
19/(-1)
-19

Therefore, -19 should be your final answer.

Answer 3

a/b = 3/5. So, assuming an integer k as the common factor, a=3k, b=5k. Then, computing (3a+2b)/(3a-2b) would give you

19k/-k = -19. Thus, the answer is -19

Answer 4

3a+2b/3a-2b
divide numerator and denominator by b so the expression becomes
[3(a/b)+2]/[3(a/b)-2]
substitute a/b=3/5
3*(3/5)+2/3(3/5)-2
=9+10/9-10
= -19

Answer 5

a/b = 3/5

(3a+2b)/(3a-2b)
= (3(a/b)+2)/(3(a/b)-2)
= 3(3/5) +2)/(3(3/5) -2)

= (3*3+2*5)/(3*3-2*5)
=(9+10)/(9-10)
= 19/(-1)
= -19

Answer 6

given:a/b=3/5
3a+2b/3a-2b
dividing numerator and denominator by a we get-
numerator=3+2b/a
subtitute value of b/a in this we get-
3+2*5/3=19/3
denominator=3-2b/a
3-2*5/3= -1/3
answer is=-19

Answer 7

If a/b=3/5,then a=3 and b=5

3(3) + 2(5) / 3(3) - 2(5) = 19 / -1 = -19

-19 not equal 3/5

therefore false

Answer 8

a/b = 3/5 then
3a + 2b/3a - 2b =
(9b/5 + 2b)/(9b/5 - 2b) =
(9 + 10)/(9 - 10) =
-19

Answer 9

a/b=3/5 solve for a

a = 3b/5 now substitute into equation (3a+2b)/(3a-2b)

(3(3b/5) +2b)/(3(3b/5 )-2b) =
(19b/5)/(-b/5) = -19

Answer 10

a=3b/5
substitute this in the given equation
3(3b/5)+2b/3(3b/5)-2b
which gives -19