Issolvi m^2+1/m+12+2/m

$$m ^ { 2 } + \frac { 1 } { m + 12 } + \frac { 2 } { m }$$

Evalwa

$$\frac{m^{4}+12m^{3}+3m+24}{m\left(m+12\right)}$$

Passi Qosra tas-Soluzzjonijiet

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika m^{2} b'\frac{m+12}{m+12}.

$$\frac{m^{2}\left(m+12\right)}{m+12}+\frac{1}{m+12}+\frac{2}{m}$$

Billi \frac{m^{2}\left(m+12\right)}{m+12} u \frac{1}{m+12} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{m^{2}\left(m+12\right)+1}{m+12}+\frac{2}{m}$$

Agħmel il-multiplikazzjonijiet fi m^{2}\left(m+12\right)+1.

$$\frac{m^{3}+12m^{2}+1}{m+12}+\frac{2}{m}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' m+12 u m huwa m\left(m+12\right). Immultiplika \frac{m^{3}+12m^{2}+1}{m+12} b'\frac{m}{m}. Immultiplika \frac{2}{m} b'\frac{m+12}{m+12}.

$$\frac{\left(m^{3}+12m^{2}+1\right)m}{m\left(m+12\right)}+\frac{2\left(m+12\right)}{m\left(m+12\right)}$$

Billi \frac{\left(m^{3}+12m^{2}+1\right)m}{m\left(m+12\right)} u \frac{2\left(m+12\right)}{m\left(m+12\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(m^{3}+12m^{2}+1\right)m+2\left(m+12\right)}{m\left(m+12\right)}$$

Agħmel il-multiplikazzjonijiet fi \left(m^{3}+12m^{2}+1\right)m+2\left(m+12\right).

$$\frac{m^{4}+12m^{3}+m+2m+24}{m\left(m+12\right)}$$

Ikkombina termini simili f'm^{4}+12m^{3}+m+2m+24.

$$\frac{m^{4}+12m^{3}+3m+24}{m\left(m+12\right)}$$

Espandi m\left(m+12\right).

$$\frac{m^{4}+12m^{3}+3m+24}{m^{2}+12m}$$

Iddifferenzja w.r.t. m

$$\frac{2m^{5}+48m^{4}+288m^{3}-3m^{2}-48m-288}{\left(m\left(m+12\right)\right)^{2}}$$