Rešite (x-2/x+1+5-x/x-2):[(1/x^2-x-2-1/x^2+3x+2)*(frac{x+1}{x}+frac{3-x^2}{x^2+x})]

$$( \frac { x - 2 } { x + 1 } + \frac { 5 - x } { x - 2 } ) : [ ( \frac { 1 } { x ^ { 2 } - x - 2 } - \frac { 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot ( \frac { x + 1 } { x } + \frac { 3 - x ^ { 2 } } { x ^ { 2 } + x } ) ]$$

Ovrednoti

$$\frac{9x\left(x+1\right)}{8}$$

Kratka navodila za rešitev

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

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

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

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

Izvedi množenje v \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).

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

Združite podobne člene v x^{2}-2x-2x+4+5x+5-x^{2}-x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktorizirajte x^{2}-x-2. Faktorizirajte x^{2}+3x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Izvedi množenje v x+2-\left(x-2\right).

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Združite podobne člene v x+2-x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktorizirajte x^{2}+x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}$$

Združite podobne člene v x^{2}+x+1+x+3-x^{2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}$$

Pomnožite \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} s/z \frac{2x+4}{x\left(x+1\right)} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}$$

Delite \frac{9}{\left(x-2\right)\left(x+1\right)} s/z \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} tako, da pomnožite \frac{9}{\left(x-2\right)\left(x+1\right)} z obratno vrednostjo \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}.

$$\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}$$

Okrajšaj \left(x-2\right)\left(x+1\right) v števcu in imenovalcu.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}$$

Okrajšaj x+2 v števcu in imenovalcu.

$$\frac{9x\left(x+1\right)}{2\times 4}$$

Razširite izraz.

$$\frac{9x^{2}+9x}{8}$$

Razširi

$$\frac{9x^{2}+9x}{8}$$

Kratka navodila za rešitev

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

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

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

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

Izvedi množenje v \left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right).

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

Združite podobne člene v x^{2}-2x-2x+4+5x+5-x^{2}-x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktorizirajte x^{2}-x-2. Faktorizirajte x^{2}+3x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Izvedi množenje v x+2-\left(x-2\right).

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Združite podobne člene v x+2-x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktorizirajte x^{2}+x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}$$

Združite podobne člene v x^{2}+x+1+x+3-x^{2}.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}$$

Pomnožite \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} s/z \frac{2x+4}{x\left(x+1\right)} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}}$$

Delite \frac{9}{\left(x-2\right)\left(x+1\right)} s/z \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} tako, da pomnožite \frac{9}{\left(x-2\right)\left(x+1\right)} z obratno vrednostjo \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}.

$$\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}$$

Okrajšaj \left(x-2\right)\left(x+1\right) v števcu in imenovalcu.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}$$

Okrajšaj x+2 v števcu in imenovalcu.

$$\frac{9x\left(x+1\right)}{2\times 4}$$

Razširite izraz.

$$\frac{9x^{2}+9x}{8}$$