**(a)** $$\frac{(x-2)(x-5)+(x-4)(x-3)}{(x-3)(x-5)}=\frac{10}{3}$$
Numerator $=(x^2-7x+10)+(x^2-7x+12)=2x^2-14x+22$
Denominator $=x^2-8x+15$
$$3(2x^2-14x+22)=10(x^2-8x+15)$$
$$6x^2-42x+66=10x^2-80x+150$$
$$4x^2-38x+84=0 \Rightarrow 2x^2-19x+42=0$$
Discriminant $=361-336=25$. $$x=\frac{19\pm5}{4} \Rightarrow x=6 \text{ or } x=\frac72$$

**(b)** Let speed of stream $=x$ km/h. Upstream speed $=20-x$, downstream speed $=20+x$.
$$\frac{48}{20-x}-\frac{48}{20+x}=1$$
$$48\left[\frac{(20+x)-(20-x)}{(20-x)(20+x)}\right]=1 \Rightarrow \frac{96x}{400-x^2}=1$$
$$96x=400-x^2 \Rightarrow x^2+96x-400=0$$
Discriminant $=9216+1600=10816=104^2$. $$x=\frac{-96+104}{2}=4$$
Speed of stream = 4 km/h.