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

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

Procijeni

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Kratki koraci rješenja

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

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x+1\right)\left(x+2\right) i \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)} i \frac{x-2}{x-2}. Pomnožite \frac{6}{\left(x-2\right)\left(-x-1\right)} i \frac{-\left(x+2\right)}{-\left(x+2\right)}.

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

Pošto \frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} i \frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Izvršite množenja u \left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right).

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

Kombinirajte slične izraze u x^{2}-2x-x+2-6x-12.

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

Faktorirajte izraze koji nisu već faktorirani u \frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}.

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

Otkaži x+1 u brojiocu i imeniocu.

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

Faktorirajte 4-x^{2}.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(x-2\right)\left(x+2\right) i \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)} i \frac{-1}{-1}.

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

Pošto \frac{x-10}{\left(x-2\right)\left(x+2\right)} i \frac{-\left(10-x\right)}{\left(x-2\right)\left(x+2\right)} imaju isti imenilac, oduzmite ih tako što ćete oduzeti njihove brojioce.

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

Izvršite množenja u x-10-\left(-\left(10-x\right)\right).

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

Kombinirajte slične izraze u x-10+10-x.

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

Nula podijeljena izrazom koji nije nula daje nulu.

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Faktor

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