Issolvi 2n/n+2n+m/2n-m+4mn/4n^2-n^2

$$\frac { 2 n } { n + 2 n } + \frac { m } { 2 n - m } + \frac { 4 m n } { 4 n ^ { 2 } - n ^ { 2 } }$$

Evalwa

$$\frac{4n^{2}+9mn-4m^{2}}{3n\left(2n-m\right)}$$

Passi Qosra tas-Soluzzjonijiet

Ikkombina n u 2n biex tikseb 3n.

$$\frac{2n}{3n}+\frac{m}{2n-m}+\frac{4mn}{4n^{2}-n^{2}}$$

Annulla n fin-numeratur u d-denominatur.

$$\frac{2}{3}+\frac{m}{2n-m}+\frac{4mn}{4n^{2}-n^{2}}$$

Ikkombina 4n^{2} u -n^{2} biex tikseb 3n^{2}.

$$\frac{2}{3}+\frac{m}{2n-m}+\frac{4mn}{3n^{2}}$$

Annulla n fin-numeratur u d-denominatur.

$$\frac{2}{3}+\frac{m}{2n-m}+\frac{4m}{3n}$$

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

$$\frac{2\left(-m+2n\right)}{3\left(-m+2n\right)}+\frac{3m}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

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

$$\frac{2\left(-m+2n\right)+3m}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

Agħmel il-multiplikazzjonijiet fi 2\left(-m+2n\right)+3m.

$$\frac{-2m+4n+3m}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

Ikkombina termini simili f'-2m+4n+3m.

$$\frac{m+4n}{3\left(-m+2n\right)}+\frac{4m}{3n}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 3\left(-m+2n\right) u 3n huwa 3n\left(-m+2n\right). Immultiplika \frac{m+4n}{3\left(-m+2n\right)} b'\frac{n}{n}. Immultiplika \frac{4m}{3n} b'\frac{-m+2n}{-m+2n}.

$$\frac{\left(m+4n\right)n}{3n\left(-m+2n\right)}+\frac{4m\left(-m+2n\right)}{3n\left(-m+2n\right)}$$

Billi \frac{\left(m+4n\right)n}{3n\left(-m+2n\right)} u \frac{4m\left(-m+2n\right)}{3n\left(-m+2n\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\left(m+4n\right)n+4m\left(-m+2n\right)}{3n\left(-m+2n\right)}$$

Agħmel il-multiplikazzjonijiet fi \left(m+4n\right)n+4m\left(-m+2n\right).

$$\frac{mn+4n^{2}-4m^{2}+8mn}{3n\left(-m+2n\right)}$$

Ikkombina termini simili f'mn+4n^{2}-4m^{2}+8mn.

$$\frac{-4m^{2}+9mn+4n^{2}}{3n\left(-m+2n\right)}$$

Espandi 3n\left(-m+2n\right).

$$\frac{-4m^{2}+9mn+4n^{2}}{-3mn+6n^{2}}$$

Iddifferenzja w.r.t. m

$$\frac{2\left(-2m^{2}+8mn-11n^{2}\right)}{3n\left(m-2n\right)\left(2n-m\right)}$$