Rešite f(x)=(x^2+4x+3/x^2+2x-3-x^2+2x+1/x^2+3x+2)*x+2/x+1

$$f ( x ) = ( \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 2 } + 2 x - 3 } - \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot \frac { x + 2 } { x + 1 }$$

Ovrednoti

$$\frac{3}{x-1}$$

Kratka navodila za rešitev

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

Okrajšaj x+3 v števcu in imenovalcu.

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

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x^{2}+2x+1}{x^{2}+3x+2}.

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

Okrajšaj x+1 v števcu in imenovalcu.

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

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

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

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

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

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

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

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

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

Pomnožite \frac{3x+3}{\left(x-1\right)\left(x+2\right)} s/z \frac{x+2}{x+1} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Okrajšaj x+2 v števcu in imenovalcu.

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

Faktorizirajte izraze, ki še niso faktorizirani.

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

Okrajšaj x+1 v števcu in imenovalcu.

$$\frac{3}{x-1}$$

Razširi

$$\frac{3}{x-1}$$

Kratka navodila za rešitev

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x^{2}+4x+3}{x^{2}+2x-3}.

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

Okrajšaj x+3 v števcu in imenovalcu.

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

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x^{2}+2x+1}{x^{2}+3x+2}.

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

Okrajšaj x+1 v števcu in imenovalcu.

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

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

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

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

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

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

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

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

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

Pomnožite \frac{3x+3}{\left(x-1\right)\left(x+2\right)} s/z \frac{x+2}{x+1} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Okrajšaj x+2 v števcu in imenovalcu.

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

Faktorizirajte izraze, ki še niso faktorizirani.

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

Okrajšaj x+1 v števcu in imenovalcu.

$$\frac{3}{x-1}$$