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

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

Izračunaj

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

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+9 i x jest x\left(x+9\right). Pomnožite \frac{1}{x+9} i \frac{x}{x}. Pomnožite \frac{1}{x} i \frac{x+9}{x+9}.

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

Budući da \frac{x}{x\left(x+9\right)} i \frac{x+9}{x\left(x+9\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x-\left(x+9\right).

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

Kombinirajte slične izraze u 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)} kao jedan razlomak.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+9 i x jest x\left(x+9\right). Pomnožite \frac{1}{x+9} i \frac{x}{x}. Pomnožite \frac{1}{x} i \frac{x+9}{x+9}.

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

Budući da \frac{x}{x\left(x+9\right)} i \frac{x+9}{x\left(x+9\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x-\left(x+9\right).

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

Kombinirajte slične izraze u 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)} kao jedan razlomak.

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

Kombinirajte \frac{4\left(-9\right)}{x\left(x+9\right)} i \frac{4\left(-9\right)}{x\left(x+9\right)} da biste dobili 2\times \frac{4\left(-9\right)}{x\left(x+9\right)}.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+9\right)^{2} i x^{2} jest x^{2}\left(x+9\right)^{2}. Pomnožite \frac{-1}{\left(x+9\right)^{2}} i \frac{x^{2}}{x^{2}}. Pomnožite \frac{1}{x^{2}} i \frac{\left(x+9\right)^{2}}{\left(x+9\right)^{2}}.

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

Budući da \frac{-x^{2}}{x^{2}\left(x+9\right)^{2}} i \frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Pomnožite izraz -x^{2}+\left(x+9\right)^{2}.

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

Kombinirajte slične izraze u -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}} kao jedan razlomak.

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

Pomnožite 4 i -9 da biste dobili -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)} kao jedan razlomak.

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

Koristite svojstvo distributivnosti da biste pomnožili 4 s 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 kao jedan razlomak.

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

Skratite x u brojniku i nazivniku.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x\left(x+9\right) i x\left(x+9\right)^{2} jest x\left(x+9\right)^{2}. Pomnožite \frac{2\left(-36\right)}{x\left(x+9\right)} i \frac{x+9}{x+9}.

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

Budući da \frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} i \frac{72x+324}{x\left(x+9\right)^{2}} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Pomnožite izraz 2\left(-36\right)\left(x+9\right)+72x+324.

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

Kombinirajte slične izraze u -72x-648+72x+324.

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

Proširivanje broja x\left(x+9\right)^{2}.

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

Proširi

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

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+9 i x jest x\left(x+9\right). Pomnožite \frac{1}{x+9} i \frac{x}{x}. Pomnožite \frac{1}{x} i \frac{x+9}{x+9}.

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

Budući da \frac{x}{x\left(x+9\right)} i \frac{x+9}{x\left(x+9\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x-\left(x+9\right).

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

Kombinirajte slične izraze u 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)} kao jedan razlomak.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x+9 i x jest x\left(x+9\right). Pomnožite \frac{1}{x+9} i \frac{x}{x}. Pomnožite \frac{1}{x} i \frac{x+9}{x+9}.

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

Budući da \frac{x}{x\left(x+9\right)} i \frac{x+9}{x\left(x+9\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Pomnožite izraz x-\left(x+9\right).

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

Kombinirajte slične izraze u 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)} kao jedan razlomak.

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

Kombinirajte \frac{4\left(-9\right)}{x\left(x+9\right)} i \frac{4\left(-9\right)}{x\left(x+9\right)} da biste dobili 2\times \frac{4\left(-9\right)}{x\left(x+9\right)}.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(x+9\right)^{2} i x^{2} jest x^{2}\left(x+9\right)^{2}. Pomnožite \frac{-1}{\left(x+9\right)^{2}} i \frac{x^{2}}{x^{2}}. Pomnožite \frac{1}{x^{2}} i \frac{\left(x+9\right)^{2}}{\left(x+9\right)^{2}}.

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

Budući da \frac{-x^{2}}{x^{2}\left(x+9\right)^{2}} i \frac{\left(x+9\right)^{2}}{x^{2}\left(x+9\right)^{2}} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Pomnožite izraz -x^{2}+\left(x+9\right)^{2}.

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

Kombinirajte slične izraze u -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}} kao jedan razlomak.

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

Pomnožite 4 i -9 da biste dobili -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)} kao jedan razlomak.

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

Koristite svojstvo distributivnosti da biste pomnožili 4 s 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 kao jedan razlomak.

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

Skratite x u brojniku i nazivniku.

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

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x\left(x+9\right) i x\left(x+9\right)^{2} jest x\left(x+9\right)^{2}. Pomnožite \frac{2\left(-36\right)}{x\left(x+9\right)} i \frac{x+9}{x+9}.

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

Budući da \frac{2\left(-36\right)\left(x+9\right)}{x\left(x+9\right)^{2}} i \frac{72x+324}{x\left(x+9\right)^{2}} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Pomnožite izraz 2\left(-36\right)\left(x+9\right)+72x+324.

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

Kombinirajte slične izraze u -72x-648+72x+324.

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

Proširivanje broja x\left(x+9\right)^{2}.

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