5) b+2b0.5c0.5+c bc0.5+b0.5c;

5) Сократим дробь:

$$\frac{b + 2b^{0.5}c^{0.5} + c}{bc^{0.5} + b^{0.5}c} = \frac{(b^{0.5})^2 + 2b^{0.5}c^{0.5} + (c^{0.5})^2}{b^{0.5}c^{0.5}(b^{0.5} + c^{0.5})} = \frac{(b^{0.5} + c^{0.5})^2}{b^{0.5}c^{0.5}(b^{0.5} + c^{0.5})} = \frac{b^{0.5} + c^{0.5}}{b^{0.5}c^{0.5}}$$

Ответ: $$\frac{b^{0.5} + c^{0.5}}{b^{0.5}c^{0.5}}$$