Rešite a+1/a^2-a-1-a/a^2+a

$$\frac { a + 1 } { a ^ { 2 } - a } - \frac { 1 - a } { a ^ { 2 } + a }$$

Ovrednoti

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

Kratka navodila za rešitev

Faktorizirajte a^{2}-a. Faktorizirajte a^{2}+a.

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

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

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

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

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

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

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

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

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

Razčlenite a\left(a-1\right)\left(a+1\right).

$$\frac{2a^{2}+2}{a^{3}-a}$$

Razširi

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

Kratka navodila za rešitev

Faktorizirajte a^{2}-a. Faktorizirajte a^{2}+a.

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

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

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

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

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

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

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

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

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

Razčlenite a\left(a-1\right)\left(a+1\right).

$$\frac{2a^{2}+2}{a^{3}-a}$$