Riješi c+12/(12-c)^2+12/12c-c^2

$$\frac { c + 12 } { ( 12 - c ) ^ { 2 } } + \frac { 12 } { 12 c - c ^ { 2 } }$$

Procijeni

$$\frac{c^{2}+144}{c\left(12-c\right)^{2}}$$

Kratki koraci rješenja

Faktorirajte 12c-c^{2}.

$$\frac{c+12}{\left(12-c\right)^{2}}+\frac{12}{c\left(-c+12\right)}$$

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(12-c\right)^{2} i c\left(-c+12\right) je c\left(-c+12\right)\left(-c+12\right)^{2}. Pomnožite \frac{c+12}{\left(12-c\right)^{2}} i \frac{c\left(-c+12\right)}{c\left(-c+12\right)}. Pomnožite \frac{12}{c\left(-c+12\right)} i \frac{\left(-c+12\right)^{2}}{\left(-c+12\right)^{2}}.

$$\frac{\left(c+12\right)c\left(-c+12\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}}+\frac{12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Pošto \frac{\left(c+12\right)c\left(-c+12\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}} i \frac{12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{\left(c+12\right)c\left(-c+12\right)+12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Izvršite množenja u \left(c+12\right)c\left(-c+12\right)+12\left(-c+12\right)^{2}.

$$\frac{-c^{3}+12c^{2}-12c^{2}+144c+12c^{2}-288c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Kombinirajte slične izraze u -c^{3}+12c^{2}-12c^{2}+144c+12c^{2}-288c+1728.

$$\frac{-c^{3}+12c^{2}-144c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Faktorirajte izraze koji nisu već faktorirani u \frac{-c^{3}+12c^{2}-144c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}.

$$\frac{\left(-c+12\right)\left(c^{2}+144\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Otkaži -c+12 u brojiocu i imeniocu.

$$\frac{c^{2}+144}{c\left(-c+12\right)^{2}}$$

Proširite c\left(-c+12\right)^{2}.

$$\frac{c^{2}+144}{c^{3}-24c^{2}+144c}$$

Proširi

$$\frac{c^{2}+144}{c\left(c-12\right)^{2}}$$

Kratki koraci rješenja

Faktorirajte 12c-c^{2}.

$$\frac{c+12}{\left(12-c\right)^{2}}+\frac{12}{c\left(-c+12\right)}$$

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(12-c\right)^{2} i c\left(-c+12\right) je c\left(-c+12\right)\left(-c+12\right)^{2}. Pomnožite \frac{c+12}{\left(12-c\right)^{2}} i \frac{c\left(-c+12\right)}{c\left(-c+12\right)}. Pomnožite \frac{12}{c\left(-c+12\right)} i \frac{\left(-c+12\right)^{2}}{\left(-c+12\right)^{2}}.

$$\frac{\left(c+12\right)c\left(-c+12\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}}+\frac{12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Pošto \frac{\left(c+12\right)c\left(-c+12\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}} i \frac{12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{\left(c+12\right)c\left(-c+12\right)+12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Izvršite množenja u \left(c+12\right)c\left(-c+12\right)+12\left(-c+12\right)^{2}.

$$\frac{-c^{3}+12c^{2}-12c^{2}+144c+12c^{2}-288c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Kombinirajte slične izraze u -c^{3}+12c^{2}-12c^{2}+144c+12c^{2}-288c+1728.

$$\frac{-c^{3}+12c^{2}-144c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Faktorirajte izraze koji nisu već faktorirani u \frac{-c^{3}+12c^{2}-144c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}.

$$\frac{\left(-c+12\right)\left(c^{2}+144\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}}$$

Otkaži -c+12 u brojiocu i imeniocu.

$$\frac{c^{2}+144}{c\left(-c+12\right)^{2}}$$

Proširite c\left(-c+12\right)^{2}.

$$\frac{c^{2}+144}{c^{3}-24c^{2}+144c}$$