Solvi għal x
x=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}
m\neq 0\text{ and }|m|\neq \frac{\sqrt{6\sqrt{17}+18}}{3}
Graff
Sehem
Ikkupjat fuq il-klibbord
\frac{1}{2}x\left(2+\frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\right)\left(6m^{2}+8\right)\times 2=m\left(3m^{2}+4\right)\sqrt{6}
Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2m\left(3m^{2}+4\right), l-inqas denominatur komuni ta' 2,2\left(3m^{2}+4\right),m.
\frac{1}{2}x\left(\frac{2\times 2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)}+\frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\right)\left(6m^{2}+8\right)\times 2=m\left(3m^{2}+4\right)\sqrt{6}
Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2 b'\frac{2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)}.
\frac{1}{2}x\times \frac{2\times 2\left(3m^{2}+4\right)+16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=m\left(3m^{2}+4\right)\sqrt{6}
Billi \frac{2\times 2\left(3m^{2}+4\right)}{2\left(3m^{2}+4\right)} u \frac{16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.
\frac{1}{2}x\times \frac{12m^{2}+16+16+24m^{2}-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=m\left(3m^{2}+4\right)\sqrt{6}
Agħmel il-multiplikazzjonijiet fi 2\times 2\left(3m^{2}+4\right)+16+24m^{2}-9m^{4}.
\frac{1}{2}x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)\times 2=m\left(3m^{2}+4\right)\sqrt{6}
Ikkombina termini simili f'12m^{2}+16+16+24m^{2}-9m^{4}.
x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)=m\left(3m^{2}+4\right)\sqrt{6}
Immultiplika \frac{1}{2} u 2 biex tikseb 1.
\frac{x\left(36m^{2}+32-9m^{4}\right)}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right)=m\left(3m^{2}+4\right)\sqrt{6}
Esprimi x\times \frac{36m^{2}+32-9m^{4}}{2\left(3m^{2}+4\right)} bħala frazzjoni waħda.
\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}=m\left(3m^{2}+4\right)\sqrt{6}
Esprimi \frac{x\left(36m^{2}+32-9m^{4}\right)}{2\left(3m^{2}+4\right)}\left(6m^{2}+8\right) bħala frazzjoni waħda.
\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}=\left(3m^{3}+4m\right)\sqrt{6}
Uża l-propjetà distributtiva biex timmultiplika m b'3m^{2}+4.
\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}=3m^{3}\sqrt{6}+4m\sqrt{6}
Uża l-propjetà distributtiva biex timmultiplika 3m^{3}+4m b'\sqrt{6}.
\frac{-2\times 9x\left(3m^{2}+4\right)\left(m^{2}-\left(-\frac{2}{3}\sqrt{17}+2\right)\right)\left(m^{2}-\left(\frac{2}{3}\sqrt{17}+2\right)\right)}{2\left(3m^{2}+4\right)}=3m^{3}\sqrt{6}+4m\sqrt{6}
Iffattura l-espressjonijiet li mhumiex diġà fatturati f'\frac{x\left(36m^{2}+32-9m^{4}\right)\left(6m^{2}+8\right)}{2\left(3m^{2}+4\right)}.
-9x\left(m^{2}-\left(-\frac{2}{3}\sqrt{17}+2\right)\right)\left(m^{2}-\left(\frac{2}{3}\sqrt{17}+2\right)\right)=3m^{3}\sqrt{6}+4m\sqrt{6}
Annulla 2\left(3m^{2}+4\right) fin-numeratur u d-denominatur.
-9xm^{4}+36xm^{2}+32x=3m^{3}\sqrt{6}+4m\sqrt{6}
Espandi l-espressjoni.
\left(-9m^{4}+36m^{2}+32\right)x=3m^{3}\sqrt{6}+4m\sqrt{6}
Ikkombina t-termini kollha li fihom x.
\left(32+36m^{2}-9m^{4}\right)x=3\sqrt{6}m^{3}+4\sqrt{6}m
L-ekwazzjoni hija f'forma standard.
\frac{\left(32+36m^{2}-9m^{4}\right)x}{32+36m^{2}-9m^{4}}=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}
Iddividi ż-żewġ naħat b'36m^{2}+32-9m^{4}.
x=\frac{\sqrt{6}m\left(3m^{2}+4\right)}{32+36m^{2}-9m^{4}}
Meta tiddividi b'36m^{2}+32-9m^{4} titneħħa l-multiplikazzjoni b'36m^{2}+32-9m^{4}.
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