Naloge

7.

a) $\displaystyle{\frac{x-3}{x}=\frac{1}{x^2-2x}-1}$

b) $\displaystyle{\frac{x+9}{x+4}-\frac{x-1}{x^2+4x}=1}$

c) $\displaystyle{1-\frac{1}{x^2+x-182}=\frac{x+13}{x+14}}$

č) $\displaystyle{\frac{x-8}{x^2-x}-\frac{1}{x^2-x}=\frac{x^2-25}{x^3+7x^2-8x}}$

Nalogo reši tudi s programom za simbolno računanje.

8.

a) $\displaystyle{\frac{14}{x^2-9}=\frac{x-2}{x+1}}$

b) $\displaystyle{\frac{x^2}{x-3}+\frac{x+4}{x+3}=\frac{x^2}{9-x^2}}$

c) $\displaystyle{\frac{x^2-x}{x-4}-\frac{2}{x+1}=\frac{10}{x^2-3x-4}}$

č) $\displaystyle{\frac{2}{x-1}-\frac{1}{x-2}=\frac{4}{x+1}-\frac{3}{x}}$

9.

a) $\displaystyle{\sqrt{\frac{x^3}{x-2}}=3\sqrt{3}}$

b) $\displaystyle{\sqrt{\frac{x^2+x}{x-1}+\frac{10x}{3(x-2)}}=x+1}$

c) $\displaystyle{\frac{x^2+1}{x+1}-9=\sqrt{\frac{x^2+1}{x+1}}-9\sqrt{\frac{x+1}{x^2+1}}}$

č) $\displaystyle{\sqrt{\frac{12x}{x^2-1}+\sqrt[3]{\frac{12x}{x^2-1}}+6}=4}$

10.

a) $\displaystyle{\frac{|x-2|}{x+1}=\frac{|x-3|}{x+4}}$

b) $\displaystyle{7^{\frac{x^2}{x-2}}=\frac{1}{7}}$

c) $\displaystyle{9^{\frac{2x-3}{x+5}}+2\cdot 3^{\frac{2x-3}{x+5}}=3}$

č) $\displaystyle{\log x^2+\frac{2}{\log x-2}=0}$