I am new to DirectX development and I am wondering if I am taking the wrong route to achieve the following:
I would like to mix three textures which contain transparent areas and some solid areas (Red, Blue, Green). The three textures should blend like shown in this example:

How can I achieve that in DirectX (preferably in directx9)?
A link or example code would be nice.
Update:
My rendering method looks like this and I still think I am doing it wrong, because the sprite only shows the last texture (nothing is rendered transparent or blended):
void D3DTester::render()
{
d3ddevice->Clear(0, NULL, D3DCLEAR_TARGET, D3DCOLOR_XRGB(0,0,0), 1.0f, 0);
d3ddevice->BeginScene();
d3ddevice->SetRenderState(D3DRS_ALPHABLENDENABLE, TRUE);
d3ddevice->SetRenderState(D3DRS_SRCBLEND, D3DBLEND_ONE);
d3ddevice->SetRenderState(D3DRS_DESTBLEND, D3DBLEND_ONE);
LPD3DXSPRITE sprite=NULL;
HRESULT hres = D3DXCreateSprite(d3ddevice, &sprite);
if(hres != S_OK)
{
throw std::exception();
}
sprite->Begin(D3DXSPRITE_ALPHABLEND);
std::vector<LPDIRECT3DTEXTURE9>::iterator it;
for ( it=textures.begin() ; it < textures.end(); it++ )
{
sprite->Draw(*it, NULL, NULL, NULL, 0xFFFFFFFF);
}
sprite->End();
d3ddevice->EndScene();
d3ddevice->Present(NULL, NULL, NULL, NULL);
}
The resulting image looks like this:

But I need it to look like this instead:

Update2:
I figured out that I have to SetRenderState after I use sprite->Begin(D3DXSPRITE_ALPHABLEND); thanks to the hint by Josh Petrie. However, by using this:
sprite->Begin(D3DXSPRITE_ALPHABLEND);
d3ddevice->SetRenderState(D3DRS_ALPHABLENDENABLE, TRUE);
d3ddevice->SetRenderState(D3DRS_SRCBLEND, D3DBLEND_ONE);
d3ddevice->SetRenderState(D3DRS_DESTBLEND, D3DBLEND_ONE);
std::vector<LPDIRECT3DTEXTURE9>::iterator it;
for ( it=textures.begin() ; it < textures.end(); it++ )
{
sprite->Draw(*it, NULL, NULL, NULL, 0xFFFFFFFF);
}
sprite->End();
The sprites colors are becoming transparent towards the background scene e.g.:
if I use d3ddevice->Clear(0, NULL, D3DCLEAR_TARGET, D3DCOLOR_XRGB(0,100,21), 1.0f, 0); the result looks like:

Is there any way to avoid that? I would like the sprites be transparent to each other but to be still solid to the background.