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.

Update3: After having sombody explained to me, how to do what @LaurentCouvidou and @JoshPetrie suggested, I have a working solution and therfore accept the answer:

d3ddevice->BeginScene();

D3DCOLOR white = D3DCOLOR_RGBA((UINT)255, (UINT)255, (UINT)255, 255);
D3DCOLOR black = D3DCOLOR_RGBA((UINT)0, (UINT)0, (UINT)0, 255);

sprite->Begin(D3DXSPRITE_ALPHABLEND);
sprite->Draw(pTextureRed, NULL, NULL, NULL, black);
sprite->Draw(pTextureGreen, NULL, NULL, NULL, black);
sprite->Draw(pTextureBlue, NULL, NULL, NULL, black);
sprite->End();       


sprite->Begin(D3DXSPRITE_ALPHABLEND);
d3ddevice->SetRenderState(D3DRS_ALPHATESTENABLE, TRUE);
d3ddevice->SetRenderState(D3DRS_BLENDOP, D3DBLENDOP_ADD);
d3ddevice->SetRenderState(D3DRS_SRCBLEND, D3DBLEND_ONE);
d3ddevice->SetRenderState(D3DRS_DESTBLEND, D3DBLEND_ONE);
sprite->Draw(pTextureRed, NULL, NULL, NULL, white);
sprite->Draw(pTextureGreen, NULL, NULL, NULL, white);
sprite->Draw(pTextureBlue, NULL, NULL, NULL, white);
sprite->End();

d3ddevice->EndScene();
d3ddevice->Present(NULL, NULL, NULL, NULL);