Rešite x-1/x^2+3x+2+6/2+x-x^2-10-x/4-x^2

$$\frac { x - 1 } { x ^ { 2 } + 3 x + 2 } + \frac { 6 } { 2 + x - x ^ { 2 } } - \frac { 10 - x } { 4 - x ^ { 2 } }$$

Ovrednoti

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Kratka navodila za rešitev

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

$$\frac{x-1}{\left(x+1\right)\left(x+2\right)}+\frac{6}{\left(x-2\right)\left(-x-1\right)}-\frac{10-x}{4-x^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x+1\right)\left(x+2\right) in \left(x-2\right)\left(-x-1\right) je \left(x-2\right)\left(x+1\right)\left(x+2\right). Pomnožite \frac{x-1}{\left(x+1\right)\left(x+2\right)} s/z \frac{x-2}{x-2}. Pomnožite \frac{6}{\left(x-2\right)\left(-x-1\right)} s/z \frac{-\left(x+2\right)}{-\left(x+2\right)}.

$$\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}+\frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} in \frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Izvedi množenje v \left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right).

$$\frac{x^{2}-2x-x+2-6x-12}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Združite podobne člene v x^{2}-2x-x+2-6x-12.

$$\frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Faktorizirajte izraze, ki še niso faktorizirani v \frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}.

$$\frac{\left(x-10\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Okrajšaj x+1 v števcu in imenovalcu.

$$\frac{x-10}{\left(x-2\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Faktorizirajte 4-x^{2}.

$$\frac{x-10}{\left(x-2\right)\left(x+2\right)}-\frac{10-x}{\left(x-2\right)\left(-x-2\right)}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x-2\right)\left(x+2\right) in \left(x-2\right)\left(-x-2\right) je \left(x-2\right)\left(x+2\right). Pomnožite \frac{10-x}{\left(x-2\right)\left(-x-2\right)} s/z \frac{-1}{-1}.

$$\frac{x-10}{\left(x-2\right)\left(x+2\right)}-\frac{-\left(10-x\right)}{\left(x-2\right)\left(x+2\right)}$$

Ker \frac{x-10}{\left(x-2\right)\left(x+2\right)} in \frac{-\left(10-x\right)}{\left(x-2\right)\left(x+2\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{x-10-\left(-\left(10-x\right)\right)}{\left(x-2\right)\left(x+2\right)}$$

Izvedi množenje v x-10-\left(-\left(10-x\right)\right).

$$\frac{x-10+10-x}{\left(x-2\right)\left(x+2\right)}$$

Združite podobne člene v x-10+10-x.

$$\frac{0}{\left(x-2\right)\left(x+2\right)}$$

Vrednost nič, deljena s poljubno vrednostjo, ki ni nič, da vrednost nič.

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Faktoriziraj

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