Rešite 4(1/x+9-1/x)+4(1/x+9-1/x)+4x(frac{-1}{(x+9)^2}+frac{1}{x^2})

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

Ovrednoti

$$-\frac{324}{x\left(x+9\right)^{2}}$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+9 in x je x\left(x+9\right). Pomnožite \frac{1}{x+9} s/z \frac{x}{x}. Pomnožite \frac{1}{x} s/z \frac{x+9}{x+9}.

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

Ker \frac{x}{x\left(x+9\right)} in \frac{x+9}{x\left(x+9\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v x-\left(x+9\right).

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

Združite podobne člene v x-x-9.

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

Izrazite 4\times \frac{-9}{x\left(x+9\right)} kot enojni ulomek.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+9 in x je x\left(x+9\right). Pomnožite \frac{1}{x+9} s/z \frac{x}{x}. Pomnožite \frac{1}{x} s/z \frac{x+9}{x+9}.

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

Ker \frac{x}{x\left(x+9\right)} in \frac{x+9}{x\left(x+9\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v x-\left(x+9\right).

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

Združite podobne člene v x-x-9.

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

Izrazite 4\times \frac{-9}{x\left(x+9\right)} kot enojni ulomek.

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

Združite \frac{4\left(-9\right)}{x\left(x+9\right)} in \frac{4\left(-9\right)}{x\left(x+9\right)}, da dobite 2\times \frac{4\left(-9\right)}{x\left(x+9\right)}.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x+9\right)^{2} in x^{2} je x^{2}\left(x+9\right)^{2}. Pomnožite \frac{-1}{\left(x+9\right)^{2}} s/z \frac{x^{2}}{x^{2}}. Pomnožite \frac{1}{x^{2}} s/z \frac{\left(x+9\right)^{2}}{\left(x+9\right)^{2}}.

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

\frac{-x^{2}}{x^{2}\left(x+9\right)^{2}} in \frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v -x^{2}+\left(x+9\right)^{2}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+x^{2}+18x+81}{x^{2}\left(x+9\right)^{2}}$$

Združite podobne člene v -x^{2}+x^{2}+18x+81.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}}$$

Izrazite 4\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}} kot enojni ulomek.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Pomnožite 4 in -9, da dobite -36.

$$2\times \frac{-36}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Izrazite 2\times \frac{-36}{x\left(x+9\right)} kot enojni ulomek.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Uporabite distributivnost, da pomnožite 4 s/z 18x+81.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x$$

Izrazite \frac{72x+324}{x^{2}\left(x+9\right)^{2}}x kot enojni ulomek.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{\left(72x+324\right)x}{x^{2}\left(x+9\right)^{2}}$$

Okrajšaj x v števcu in imenovalcu.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x\left(x+9\right) in x\left(x+9\right)^{2} je x\left(x+9\right)^{2}. Pomnožite \frac{2\left(-36\right)}{x\left(x+9\right)} s/z \frac{x+9}{x+9}.

$$\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} in \frac{72x+324}{x\left(x+9\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{2\left(-36\right)\left(x+9\right)+72x+324}{x\left(x+9\right)^{2}}$$

Izvedi množenje v 2\left(-36\right)\left(x+9\right)+72x+324.

$$\frac{-72x-648+72x+324}{x\left(x+9\right)^{2}}$$

Združite podobne člene v -72x-648+72x+324.

$$\frac{-324}{x\left(x+9\right)^{2}}$$

Razčlenite x\left(x+9\right)^{2}.

$$\frac{-324}{x^{3}+18x^{2}+81x}$$

Razširi

$$-\frac{324}{x\left(x+9\right)^{2}}$$

Kratka navodila za rešitev

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+9 in x je x\left(x+9\right). Pomnožite \frac{1}{x+9} s/z \frac{x}{x}. Pomnožite \frac{1}{x} s/z \frac{x+9}{x+9}.

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

Ker \frac{x}{x\left(x+9\right)} in \frac{x+9}{x\left(x+9\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v x-\left(x+9\right).

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

Združite podobne člene v x-x-9.

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

Izrazite 4\times \frac{-9}{x\left(x+9\right)} kot enojni ulomek.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x+9 in x je x\left(x+9\right). Pomnožite \frac{1}{x+9} s/z \frac{x}{x}. Pomnožite \frac{1}{x} s/z \frac{x+9}{x+9}.

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

Ker \frac{x}{x\left(x+9\right)} in \frac{x+9}{x\left(x+9\right)} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Izvedi množenje v x-\left(x+9\right).

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

Združite podobne člene v x-x-9.

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

Izrazite 4\times \frac{-9}{x\left(x+9\right)} kot enojni ulomek.

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

Združite \frac{4\left(-9\right)}{x\left(x+9\right)} in \frac{4\left(-9\right)}{x\left(x+9\right)}, da dobite 2\times \frac{4\left(-9\right)}{x\left(x+9\right)}.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(x+9\right)^{2} in x^{2} je x^{2}\left(x+9\right)^{2}. Pomnožite \frac{-1}{\left(x+9\right)^{2}} s/z \frac{x^{2}}{x^{2}}. Pomnožite \frac{1}{x^{2}} s/z \frac{\left(x+9\right)^{2}}{\left(x+9\right)^{2}}.

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

\frac{-x^{2}}{x^{2}\left(x+9\right)^{2}} in \frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v -x^{2}+\left(x+9\right)^{2}.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{-x^{2}+x^{2}+18x+81}{x^{2}\left(x+9\right)^{2}}$$

Združite podobne člene v -x^{2}+x^{2}+18x+81.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+4x\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}}$$

Izrazite 4\times \frac{18x+81}{x^{2}\left(x+9\right)^{2}} kot enojni ulomek.

$$2\times \frac{4\left(-9\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Pomnožite 4 in -9, da dobite -36.

$$2\times \frac{-36}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Izrazite 2\times \frac{-36}{x\left(x+9\right)} kot enojni ulomek.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{4\left(18x+81\right)}{x^{2}\left(x+9\right)^{2}}x$$

Uporabite distributivnost, da pomnožite 4 s/z 18x+81.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x^{2}\left(x+9\right)^{2}}x$$

Izrazite \frac{72x+324}{x^{2}\left(x+9\right)^{2}}x kot enojni ulomek.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{\left(72x+324\right)x}{x^{2}\left(x+9\right)^{2}}$$

Okrajšaj x v števcu in imenovalcu.

$$\frac{2\left(-36\right)}{x\left(x+9\right)}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik x\left(x+9\right) in x\left(x+9\right)^{2} je x\left(x+9\right)^{2}. Pomnožite \frac{2\left(-36\right)}{x\left(x+9\right)} s/z \frac{x+9}{x+9}.

$$\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}}+\frac{72x+324}{x\left(x+9\right)^{2}}$$

\frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} in \frac{72x+324}{x\left(x+9\right)^{2}} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{2\left(-36\right)\left(x+9\right)+72x+324}{x\left(x+9\right)^{2}}$$

Izvedi množenje v 2\left(-36\right)\left(x+9\right)+72x+324.

$$\frac{-72x-648+72x+324}{x\left(x+9\right)^{2}}$$

Združite podobne člene v -72x-648+72x+324.

$$\frac{-324}{x\left(x+9\right)^{2}}$$

Razčlenite x\left(x+9\right)^{2}.

$$\frac{-324}{x^{3}+18x^{2}+81x}$$