Question

\(B=\frac{3\sqrt{x}+4}{3\sqrt{x}-2}-\frac{42\sqrt{x}+34}{15x+11\sqrt{x}-14}\)

Answer 1

B=\(\frac{3\sqrt{x}+4}{3\sqrt{x}-2}-\frac{42\sqrt{x}+34}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}=\frac{(3\sqrt{x}+4)(5\sqrt{x}+7)-42\sqrt{x}-34}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}=\frac{15x+20\sqrt{x}+21\sqrt{x}+28-42\sqrt{x}-34}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}=\frac{15x-\sqrt{x}-6}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}=\frac{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+3\right)}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}=\frac{5\sqrt{x}+3}{5\sqrt{x}+7}\)