Løs c+12/(12-c)^2+12/12c-c^2

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

Evaluer

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

Korte løsningstrin

Faktoriser 12c-c^{2}.

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

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for \left(12-c\right)^{2} og c\left(-c+12\right) er c\left(-c+12\right)\left(-c+12\right)^{2}. Multiplicer \frac{c+12}{\left(12-c\right)^{2}} gange \frac{c\left(-c+12\right)}{c\left(-c+12\right)}. Multiplicer \frac{12}{c\left(-c+12\right)} gange \frac{\left(-c+12\right)^{2}}{\left(-c+12\right)^{2}}.

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

Da \frac{\left(c+12\right)c\left(-c+12\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}} og \frac{12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.

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

Lav multiplikationerne i \left(c+12\right)c\left(-c+12\right)+12\left(-c+12\right)^{2}.

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

Kombiner ens led i -c^{3}+12c^{2}-12c^{2}+144c+12c^{2}-288c+1728.

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

Faktoriser de udtryk, der ikke allerede er faktoriseret i \frac{-c^{3}+12c^{2}-144c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}.

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

Udlign -c+12 i både tælleren og nævneren.

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

Udvid c\left(-c+12\right)^{2}.

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

Udvid

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

Korte løsningstrin

Faktoriser 12c-c^{2}.

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

For tilføje eller fratrække udtryk skal du udvide dem for at gøre nævneren ens. Mindste fælles multiplum for \left(12-c\right)^{2} og c\left(-c+12\right) er c\left(-c+12\right)\left(-c+12\right)^{2}. Multiplicer \frac{c+12}{\left(12-c\right)^{2}} gange \frac{c\left(-c+12\right)}{c\left(-c+12\right)}. Multiplicer \frac{12}{c\left(-c+12\right)} gange \frac{\left(-c+12\right)^{2}}{\left(-c+12\right)^{2}}.

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

Da \frac{\left(c+12\right)c\left(-c+12\right)}{c\left(-c+12\right)\left(-c+12\right)^{2}} og \frac{12\left(-c+12\right)^{2}}{c\left(-c+12\right)\left(-c+12\right)^{2}} har den samme fællesnævner, skal du addere dem ved at tilføje deres tællere.

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

Lav multiplikationerne i \left(c+12\right)c\left(-c+12\right)+12\left(-c+12\right)^{2}.

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

Kombiner ens led i -c^{3}+12c^{2}-12c^{2}+144c+12c^{2}-288c+1728.

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

Faktoriser de udtryk, der ikke allerede er faktoriseret i \frac{-c^{3}+12c^{2}-144c+1728}{c\left(-c+12\right)\left(-c+12\right)^{2}}.

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

Udlign -c+12 i både tælleren og nævneren.

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

Udvid c\left(-c+12\right)^{2}.

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