Rešite 2/x(x-1)-5/x^2(x-1)+3/(x-1)(x+1)

$$\frac { 2 } { x ( x - 1 ) } - \frac { 5 } { x ^ { 2 } ( x - 1 ) } + \frac { 3 } { ( x - 1 ) ( x + 1 ) }$$

Ovrednoti

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x\left(x-1\right) in x^{2}\left(x-1\right) je \left(x-1\right)x^{2}. Pomnožite \frac{2}{x\left(x-1\right)} s/z \frac{x}{x}.

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

Ker \frac{2x}{\left(x-1\right)x^{2}} in \frac{5}{\left(x-1\right)x^{2}} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-1\right)x^{2} in \left(x-1\right)\left(x+1\right) je \left(x-1\right)\left(x+1\right)x^{2}. Pomnožite \frac{2x-5}{\left(x-1\right)x^{2}} s/z \frac{x+1}{x+1}. Pomnožite \frac{3}{\left(x-1\right)\left(x+1\right)} s/z \frac{x^{2}}{x^{2}}.

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

\frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}} in \frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v \left(2x-5\right)\left(x+1\right)+3x^{2}.

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

Združite podobne člene v 2x^{2}+2x-5x-5+3x^{2}.

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

Razčlenite \left(x-1\right)\left(x+1\right)x^{2}.

$$\frac{5x^{2}-3x-5}{x^{4}-x^{2}}$$

Razširi

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

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x\left(x-1\right) in x^{2}\left(x-1\right) je \left(x-1\right)x^{2}. Pomnožite \frac{2}{x\left(x-1\right)} s/z \frac{x}{x}.

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

Ker \frac{2x}{\left(x-1\right)x^{2}} in \frac{5}{\left(x-1\right)x^{2}} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-1\right)x^{2} in \left(x-1\right)\left(x+1\right) je \left(x-1\right)\left(x+1\right)x^{2}. Pomnožite \frac{2x-5}{\left(x-1\right)x^{2}} s/z \frac{x+1}{x+1}. Pomnožite \frac{3}{\left(x-1\right)\left(x+1\right)} s/z \frac{x^{2}}{x^{2}}.

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

\frac{\left(2x-5\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)x^{2}} in \frac{3x^{2}}{\left(x-1\right)\left(x+1\right)x^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v \left(2x-5\right)\left(x+1\right)+3x^{2}.

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

Združite podobne člene v 2x^{2}+2x-5x-5+3x^{2}.

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

Razčlenite \left(x-1\right)\left(x+1\right)x^{2}.

$$\frac{5x^{2}-3x-5}{x^{4}-x^{2}}$$