matematikk.net

[tex]\frac{2}{x} + \frac{3}{{x + 1}} + \frac{3}{{x(x + 1)}}[/tex]

[tex]\frac{2}{x} + \frac{3}{{x + 1}} + \frac{3}{{x(x + 1)}} = \frac{2 \cdot (x+1)}{x(x+1)} + \frac{3 \cdot x}{x(x+1)} + \frac {3}{x(x+1)} = \frac{2x +2 + 3x +3}{x(x+1)} = \frac{5x + 5}{x(x+1)} = \frac{5(x+1) }{x(x+1)} = \underline{\underline {\frac5x}}[/tex]

[tex]\frac{2}{x} \;+\; \frac{3}{x \:+\: 1} \;+\; \frac{3}{x(x \:+\: 1)}[/tex] (Her er x(x + 1) en fellesnevner)

[tex]= \; \frac{2(x \:+\: 1)}{x(x \:+\: 1)} \;+\; \frac{3x}{x(x \:+\: 1)} \;+\; \frac{3}{x(x \:+\: 1)}[/tex] (Utvider brøkene slik at alle tre får nevneren x(x + 1))

[tex]= \; \frac{2x \:+\: 2 \:+\: 3x \:+\: 3}{x(x \:+\: 1)}[/tex]

[tex]= \; \frac{5x \:+\: 5}{x(x \:+\: 1)}[/tex]

[tex]= \; \frac{5(x \:+\: 1)}{x(x \:+\: 1)}[/tex] (forkorter i teller og nevner med x + 1)

[tex]= \; \frac{5}{x} \, .[/tex]