Independence of linear combinations of Brownian motions Let $0&lt;s\leq t\leq u\leq v$ and $W_x$ be a Brownian motion. Show that $aW_s+bW_t$ and $\frac{1}{v}W_v-\frac{1}{u}W_u$ are independent for $a,b$ satisfying $as+bt=0$.

The question seems easy but somehow I can't rearrange the terms to show the independence. I know that increments of Brownian motion are independent, so I tried to add, subtract, multiply, divide  but I didn't manage to make these increments appear. For example $aW_s+bW_t=aW_s+bW_t -(as+bt)W_s$ or $aW_s+bW_t=aW_s+bW_t -(as+bt)W_t$ don't lead me anywhere. 

Thank you
Independence is equivalent to zero covariance when normals are jointly normal. So just compute the expectation of the product and see if it's zero.
Independence is equivalent to zero covariance when normals are jointly normal. So just compute the expectation of the product and see if it's zero.