Rešite 5/9/x+13/4/x+3+-23/3/(x+3)^2

$$\frac { 5 / 9 } { x } + \frac { 13 / 4 } { x + 3 } + \frac { - 23 / 3 } { ( x + 3 ) ^ { 2 } }$$

Ovrednoti

$$\frac{137x^{2}+195x+180}{36x\left(x+3\right)^{2}}$$

Kratka navodila za rešitev

Izrazite \frac{\frac{5}{9}}{x} kot enojni ulomek.

$$\frac{5}{9x}+\frac{\frac{13}{4}}{x+3}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Izrazite \frac{\frac{13}{4}}{x+3} kot enojni ulomek.

$$\frac{5}{9x}+\frac{13}{4\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 9x in 4\left(x+3\right) je 36x\left(x+3\right). Pomnožite \frac{5}{9x} s/z \frac{4\left(x+3\right)}{4\left(x+3\right)}. Pomnožite \frac{13}{4\left(x+3\right)} s/z \frac{9x}{9x}.

$$\frac{5\times 4\left(x+3\right)}{36x\left(x+3\right)}+\frac{13\times 9x}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

\frac{5\times 4\left(x+3\right)}{36x\left(x+3\right)} in \frac{13\times 9x}{36x\left(x+3\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{5\times 4\left(x+3\right)+13\times 9x}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Izvedi množenje v 5\times 4\left(x+3\right)+13\times 9x.

$$\frac{20x+60+117x}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Združite podobne člene v 20x+60+117x.

$$\frac{137x+60}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Uporabite distributivnost, da pomnožite 36x s/z x+3.

$$\frac{137x+60}{36x^{2}+108x}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Izrazite \frac{-\frac{23}{3}}{\left(x+3\right)^{2}} kot enojni ulomek.

$$\frac{137x+60}{36x^{2}+108x}+\frac{-23}{3\left(x+3\right)^{2}}$$

Faktorizirajte 36x^{2}+108x.

$$\frac{137x+60}{36x\left(x+3\right)}+\frac{-23}{3\left(x+3\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 36x\left(x+3\right) in 3\left(x+3\right)^{2} je 36x\left(x+3\right)^{2}. Pomnožite \frac{137x+60}{36x\left(x+3\right)} s/z \frac{x+3}{x+3}. Pomnožite \frac{-23}{3\left(x+3\right)^{2}} s/z \frac{12x}{12x}.

$$\frac{\left(137x+60\right)\left(x+3\right)}{36x\left(x+3\right)^{2}}+\frac{-23\times 12x}{36x\left(x+3\right)^{2}}$$

\frac{\left(137x+60\right)\left(x+3\right)}{36x\left(x+3\right)^{2}} in \frac{-23\times 12x}{36x\left(x+3\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\left(137x+60\right)\left(x+3\right)-23\times 12x}{36x\left(x+3\right)^{2}}$$

Izvedi množenje v \left(137x+60\right)\left(x+3\right)-23\times 12x.

$$\frac{137x^{2}+411x+60x+180-276x}{36x\left(x+3\right)^{2}}$$

Združite podobne člene v 137x^{2}+411x+60x+180-276x.

$$\frac{137x^{2}+195x+180}{36x\left(x+3\right)^{2}}$$

Razčlenite 36x\left(x+3\right)^{2}.

$$\frac{137x^{2}+195x+180}{36x^{3}+216x^{2}+324x}$$

Razširi

$$\frac{137x^{2}+195x+180}{36x\left(x+3\right)^{2}}$$

Kratka navodila za rešitev

Izrazite \frac{\frac{5}{9}}{x} kot enojni ulomek.

$$\frac{5}{9x}+\frac{\frac{13}{4}}{x+3}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Izrazite \frac{\frac{13}{4}}{x+3} kot enojni ulomek.

$$\frac{5}{9x}+\frac{13}{4\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 9x in 4\left(x+3\right) je 36x\left(x+3\right). Pomnožite \frac{5}{9x} s/z \frac{4\left(x+3\right)}{4\left(x+3\right)}. Pomnožite \frac{13}{4\left(x+3\right)} s/z \frac{9x}{9x}.

$$\frac{5\times 4\left(x+3\right)}{36x\left(x+3\right)}+\frac{13\times 9x}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

\frac{5\times 4\left(x+3\right)}{36x\left(x+3\right)} in \frac{13\times 9x}{36x\left(x+3\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{5\times 4\left(x+3\right)+13\times 9x}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Izvedi množenje v 5\times 4\left(x+3\right)+13\times 9x.

$$\frac{20x+60+117x}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Združite podobne člene v 20x+60+117x.

$$\frac{137x+60}{36x\left(x+3\right)}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Uporabite distributivnost, da pomnožite 36x s/z x+3.

$$\frac{137x+60}{36x^{2}+108x}+\frac{-\frac{23}{3}}{\left(x+3\right)^{2}}$$

Izrazite \frac{-\frac{23}{3}}{\left(x+3\right)^{2}} kot enojni ulomek.

$$\frac{137x+60}{36x^{2}+108x}+\frac{-23}{3\left(x+3\right)^{2}}$$

Faktorizirajte 36x^{2}+108x.

$$\frac{137x+60}{36x\left(x+3\right)}+\frac{-23}{3\left(x+3\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik 36x\left(x+3\right) in 3\left(x+3\right)^{2} je 36x\left(x+3\right)^{2}. Pomnožite \frac{137x+60}{36x\left(x+3\right)} s/z \frac{x+3}{x+3}. Pomnožite \frac{-23}{3\left(x+3\right)^{2}} s/z \frac{12x}{12x}.

$$\frac{\left(137x+60\right)\left(x+3\right)}{36x\left(x+3\right)^{2}}+\frac{-23\times 12x}{36x\left(x+3\right)^{2}}$$

\frac{\left(137x+60\right)\left(x+3\right)}{36x\left(x+3\right)^{2}} in \frac{-23\times 12x}{36x\left(x+3\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\left(137x+60\right)\left(x+3\right)-23\times 12x}{36x\left(x+3\right)^{2}}$$

Izvedi množenje v \left(137x+60\right)\left(x+3\right)-23\times 12x.

$$\frac{137x^{2}+411x+60x+180-276x}{36x\left(x+3\right)^{2}}$$

Združite podobne člene v 137x^{2}+411x+60x+180-276x.

$$\frac{137x^{2}+195x+180}{36x\left(x+3\right)^{2}}$$

Razčlenite 36x\left(x+3\right)^{2}.

$$\frac{137x^{2}+195x+180}{36x^{3}+216x^{2}+324x}$$