KF – naloga 8 – Mate(j)matika

a) $\left(\frac{\left(x-1\right)^2}{5}+1\right)\left(\frac{\left(x-1\right)^2}{5}-3\right)=4\left(\frac{\left(x-1\right)^2}{5}-3\right)+4$

b) $\frac{2}{x+1}-\frac{1}{x+4}=\frac{x^2+7x}{x^2+5x+4}$

c) $\frac{2x}{x+3}-\frac{1}{x+2}=\frac{x^2+x}{x^2+5x+6}$

a) Uvedi novo spremenljivko $t=\frac{\left(x-1\right)^2}{5}.$

b,c) Razstavi imenovalec na desni in enačbo pomnoži s skupnim imenovalcem.

a) $x_{1}=-\sqrt{5}+1,\:x_{2}=\sqrt{5}+1,\:x_{3}=-4,\:x_{4}=6$

b) $x=1,\:x=-7$

c) $x=1$