How do you solve `3/5=6/(x+3)`?

Multiply each side of the equation by `color(red)(5)(color(blue)(x + 3))` to eliminate the fractions while keeping the equation balanced:

`color(red)(5)(color(blue)(x + 3)) xx 3/5 = color(red)(5)(color(blue)(x + 3)) xx 6/(x + 3)`

`cancel(color(red)(5))(color(blue)(x + 3)) xx 3/color(red)(cancel(color(black)(5))) = color(red)(5)cancel((color(blue)(x + 3))) xx 6/color(blue)(cancel(color(black)(x + 3)))`

`3(color(blue)(x + 3)) = color(red)(5) xx 6`

`(3 xx color(blue)(x)) + (3 xx color(blue)(3)) = 30`

`3x + 9 = 30`

Next, subtract `color(red)(9)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`3x + 9 - color(red)(9) = 30 - color(red)(9)`

`3x + 0 = 21`

`3x = 21`

Now, divide each side of the equation by `color(red)(3)` to solve for `x` while keeping the equation balanced:

`(3x)/color(red)(3) = 21/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 7`

`x = 7`

Since we have two fractions on either side of an equal sign, this designates that we can cross multiply here. So, let's multiply `3` by `x+3` and `5` by `6`.

`3(x+3)` gives us `3x+9` and `5xx6` gives us `30`. Then we just solve:

`3x+9=30`

Subtract `9` from both sides:

`3x=21`

Divide by `3` on both sides:

`x=7`

Hope this helps!