Riješi (x/x+1-x/x-1)1-x^2/2

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

Procijeni

$$x$$

Kratki koraci rješenja

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

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

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

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

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

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

Kombinirajte slične izraze u x^{2}-x-x^{2}-x.

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

Pomnožite \frac{-2x}{\left(x-1\right)\left(x+1\right)} i \frac{1-x^{2}}{2} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

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

Otkaži 2 u brojiocu i imeniocu.

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

Faktorirajte izraze koji nisu već faktorirani.

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

Izdvojite znak negacije u -1-x.

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

Otkaži \left(x-1\right)\left(x+1\right) u brojiocu i imeniocu.

$$-\left(-1\right)x$$

Razvijte izraz.

$$x$$

Razlikovanje u pogledu x

$$1$$

Koraci pomoću definicije izvedenog broja

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

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

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

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

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

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

Kombinirajte slične izraze u x^{2}-x-x^{2}-x.

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

Pomnožite \frac{-2x}{\left(x-1\right)\left(x+1\right)} i \frac{1-x^{2}}{2} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

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

Otkaži 2 u brojiocu i imeniocu.

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

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

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

Izdvojite znak negacije u -1-x.

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

Otkaži \left(x-1\right)\left(x+1\right) u brojiocu i imeniocu.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(-1\right)x)$$

Razvijte izraz.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

Izvedena vrijednost broja ax^{n} je nax^{n-1}.

$$x^{1-1}$$

Oduzmite 1 od 1.

$$x^{0}$$

Za bilo koji izraz t izuzev 0, t^{0}=1.

$$1$$