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

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

Ovrednoti

$$\frac{x^{2}}{3}$$

Kratka navodila za rešitev

Uporabite lastnost distributivnosti za množenje x+3 krat x+4 in kombiniranje pogojev podobnosti.

$$\frac{x^{2}+7x+12}{\left(x+1\right)\left(x-1\right)}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

Razmislite o \left(x+1\right)\left(x-1\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrat števila 1.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

Uporabite distributivnost, da pomnožite x^{2} s/z 1+x.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

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

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3x+9}$$

Pomnožite \frac{x^{2}+7x+12}{x^{2}-1} s/z \frac{x^{2}+x^{3}}{x+4} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)}\times \frac{x-1}{3x+9}$$

Pomnožite \frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)} s/z \frac{x-1}{3x+9} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)\left(x-1\right)}{\left(x^{2}-1\right)\left(x+4\right)\left(3x+9\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani.

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

Okrajšaj \left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+4\right) v števcu in imenovalcu.

$$\frac{x^{2}}{3}$$

Razširi

$$\frac{x^{2}}{3}$$

Kratka navodila za rešitev

Uporabite lastnost distributivnosti za množenje x+3 krat x+4 in kombiniranje pogojev podobnosti.

$$\frac{x^{2}+7x+12}{\left(x+1\right)\left(x-1\right)}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

Razmislite o \left(x+1\right)\left(x-1\right). Množenje je lahko preoblikovano v razliko kvadratov s pravilom: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Kvadrat števila 1.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}\left(1+x\right)}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

Uporabite distributivnost, da pomnožite x^{2} s/z 1+x.

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3\left(x+3\right)}$$

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

$$\frac{x^{2}+7x+12}{x^{2}-1}\times \frac{x^{2}+x^{3}}{x+4}\times \frac{x-1}{3x+9}$$

Pomnožite \frac{x^{2}+7x+12}{x^{2}-1} s/z \frac{x^{2}+x^{3}}{x+4} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)}\times \frac{x-1}{3x+9}$$

Pomnožite \frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)}{\left(x^{2}-1\right)\left(x+4\right)} s/z \frac{x-1}{3x+9} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\left(x^{2}+7x+12\right)\left(x^{2}+x^{3}\right)\left(x-1\right)}{\left(x^{2}-1\right)\left(x+4\right)\left(3x+9\right)}$$

Faktorizirajte izraze, ki še niso faktorizirani.

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

Okrajšaj \left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+4\right) v števcu in imenovalcu.

$$\frac{x^{2}}{3}$$