Issolvi 1/m-n-1/m+n:2/3m-3n

$$\frac { 1 } { m - n } - \frac { 1 } { m + n } : \frac { 2 } { 3 m - 3 n }$$

Evalwa

$$\frac{2n-3n^{2}+2m+6mn-3m^{2}}{2\left(m^{2}-n^{2}\right)}$$

Passi Qosra tas-Soluzzjonijiet

Iddividi \frac{1}{m+n} b'\frac{2}{3m-3n} billi timmultiplika \frac{1}{m+n} bir-reċiproku ta' \frac{2}{3m-3n}.

$$\frac{1}{m-n}-\frac{3m-3n}{\left(m+n\right)\times 2}$$

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

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

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

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

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

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

Ikkombina termini simili f'2m+2n-3m^{2}+3mn+3nm-3n^{2}.

$$\frac{2m+2n-3m^{2}-3n^{2}+6mn}{2\left(m+n\right)\left(m-n\right)}$$

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

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

Fattur

$$\frac{2n-3n^{2}+2m+6mn-3m^{2}}{2\left(m-n\right)\left(m+n\right)}$$