Issolvi 6m+mn/4mdivn^2-36

$$\frac { 6 m + m n } { 4 m } \div n ^ { 2 } - 36$$

Evalwa

$$-36+\frac{1}{4n}+\frac{3}{2n^{2}}$$

Passi Qosra tas-Soluzzjonijiet

Esprimi \frac{\frac{6m+mn}{4m}}{n^{2}} bħala frazzjoni waħda.

$$\frac{6m+mn}{4mn^{2}}-36$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{6m+mn}{4mn^{2}}.

$$\frac{m\left(n+6\right)}{4mn^{2}}-36$$

Annulla m fin-numeratur u d-denominatur.

$$\frac{n+6}{4n^{2}}-36$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 36 b'\frac{4n^{2}}{4n^{2}}.

$$\frac{n+6}{4n^{2}}-\frac{36\times 4n^{2}}{4n^{2}}$$

Billi \frac{n+6}{4n^{2}} u \frac{36\times 4n^{2}}{4n^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{n+6-36\times 4n^{2}}{4n^{2}}$$

Agħmel il-multiplikazzjonijiet fi n+6-36\times 4n^{2}.

$$\frac{n+6-144n^{2}}{4n^{2}}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{n+6-144n^{2}}{4n^{2}}.

$$\frac{-144\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{4n^{2}}$$

Annulla 4 fin-numeratur u d-denominatur.

$$\frac{-36\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Biex issib l-oppost ta' -\frac{1}{288}\sqrt{3457}+\frac{1}{288}, sib l-oppost ta' kull terminu.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Biex issib l-oppost ta' \frac{1}{288}\sqrt{3457}+\frac{1}{288}, sib l-oppost ta' kull terminu.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Uża l-propjetà distributtiva biex timmultiplika -36 b'n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}.

$$\frac{\left(-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Uża l-propjetà distributtiva biex timmultiplika -36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8} b'n-\frac{1}{288}\sqrt{3457}-\frac{1}{288} u kkombina termini simili.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\left(\sqrt{3457}\right)^{2}-\frac{1}{2304}}{n^{2}}$$

Il-kwadrat ta' \sqrt{3457} huwa 3457.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\times 3457-\frac{1}{2304}}{n^{2}}$$

Immultiplika \frac{1}{2304} u 3457 biex tikseb \frac{3457}{2304}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3457}{2304}-\frac{1}{2304}}{n^{2}}$$

Naqqas \frac{1}{2304} minn \frac{3457}{2304} biex tikseb \frac{3}{2}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3}{2}}{n^{2}}$$

Espandi

$$-36+\frac{1}{4n}+\frac{3}{2n^{2}}$$

Passi Qosra tas-Soluzzjonijiet

Esprimi \frac{\frac{6m+mn}{4m}}{n^{2}} bħala frazzjoni waħda.

$$\frac{6m+mn}{4mn^{2}}-36$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{6m+mn}{4mn^{2}}.

$$\frac{m\left(n+6\right)}{4mn^{2}}-36$$

Annulla m fin-numeratur u d-denominatur.

$$\frac{n+6}{4n^{2}}-36$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 36 b'\frac{4n^{2}}{4n^{2}}.

$$\frac{n+6}{4n^{2}}-\frac{36\times 4n^{2}}{4n^{2}}$$

Billi \frac{n+6}{4n^{2}} u \frac{36\times 4n^{2}}{4n^{2}} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{n+6-36\times 4n^{2}}{4n^{2}}$$

Agħmel il-multiplikazzjonijiet fi n+6-36\times 4n^{2}.

$$\frac{n+6-144n^{2}}{4n^{2}}$$

Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{n+6-144n^{2}}{4n^{2}}.

$$\frac{-144\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{4n^{2}}$$

Annulla 4 fin-numeratur u d-denominatur.

$$\frac{-36\left(n-\left(-\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Biex issib l-oppost ta' -\frac{1}{288}\sqrt{3457}+\frac{1}{288}, sib l-oppost ta' kull terminu.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\left(\frac{1}{288}\sqrt{3457}+\frac{1}{288}\right)\right)}{n^{2}}$$

Biex issib l-oppost ta' \frac{1}{288}\sqrt{3457}+\frac{1}{288}, sib l-oppost ta' kull terminu.

$$\frac{-36\left(n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Uża l-propjetà distributtiva biex timmultiplika -36 b'n+\frac{1}{288}\sqrt{3457}-\frac{1}{288}.

$$\frac{\left(-36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8}\right)\left(n-\frac{1}{288}\sqrt{3457}-\frac{1}{288}\right)}{n^{2}}$$

Uża l-propjetà distributtiva biex timmultiplika -36n-\frac{1}{8}\sqrt{3457}+\frac{1}{8} b'n-\frac{1}{288}\sqrt{3457}-\frac{1}{288} u kkombina termini simili.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\left(\sqrt{3457}\right)^{2}-\frac{1}{2304}}{n^{2}}$$

Il-kwadrat ta' \sqrt{3457} huwa 3457.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{1}{2304}\times 3457-\frac{1}{2304}}{n^{2}}$$

Immultiplika \frac{1}{2304} u 3457 biex tikseb \frac{3457}{2304}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3457}{2304}-\frac{1}{2304}}{n^{2}}$$

Naqqas \frac{1}{2304} minn \frac{3457}{2304} biex tikseb \frac{3}{2}.

$$\frac{-36n^{2}+\frac{1}{4}n+\frac{3}{2}}{n^{2}}$$