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a,12x-180+10x-20+39x-2340+65x-4420=780
126x-6960=780
126x=7740
x=430/7
\(5x-200=\frac{5x}{2}-300+2x+300\)0
\(3x-2,5x=200\)\(0,5x=200\)\(x=400\)
=>\(\frac{30x\left(x-6\right)}{x\left(x+10\right)\left(x-6\right)}+\frac{30x\left(x+10\right)}{x\left(x+10\right)\left(x-6\right)}=\frac{60\left(x+10\right)\left(x-6\right)}{x\left(x-6\left(x+10\right)\right)}\)
=>30x2-180x+30x2+300x=60x2-360x+600x-3600
=>60x2+120x=60x2+240x-3600
=>-120x=-3600
=>x=30
nhớ k mk........Đúng 100%
\(\sqrt{\frac{42}{5-x}}+\sqrt{\frac{60}{7-x}}=6\)
\(\Leftrightarrow\sqrt{\frac{42}{5-x}}-\sqrt{\frac{126}{14}}+\sqrt{\frac{60}{7-x}}-\sqrt{\frac{45}{5}}=0\)
\(\Leftrightarrow\frac{\frac{42}{5-x}-\frac{126}{14}}{\sqrt{\frac{42}{5-x}}+\sqrt{\frac{126}{14}}}+\frac{\frac{60}{7-x}-\frac{45}{5}}{\sqrt{\frac{60}{7-x}}+\sqrt{\frac{45}{5}}}=0\)
\(\Leftrightarrow\frac{\frac{-3\left(3x-1\right)}{x-5}}{\sqrt{\frac{42}{5-x}}+\sqrt{\frac{126}{14}}}+\frac{\frac{-3\left(3x-1\right)}{x-7}}{\sqrt{\frac{60}{7-x}}+\sqrt{\frac{45}{5}}}=0\)
\(\Leftrightarrow-3\left(3x-1\right)\left(\frac{\frac{1}{x-5}}{\sqrt{\frac{42}{x-5}}+\sqrt{\frac{126}{14}}}+\frac{\frac{1}{x-7}}{\sqrt{\frac{60}{7-x}}+\sqrt{\frac{45}{5}}}\right)=0\)
Dễ thấy : \(\frac{\frac{1}{x-5}}{\sqrt{\frac{42}{5-x}}+\sqrt{\frac{126}{14}}}+\frac{\frac{1}{x-7}}{\sqrt{\frac{60}{7-x}}+\sqrt{\frac{45}{5}}}>0\)
\(\Rightarrow3x-1=0\Rightarrow x=\frac{1}{3}\)
Chúc bạn học tốt !!!
\(ĐK:x\ne0;x\ne-6\)
⇔ \(\frac{720\left(x+6\right)}{6x\left(x+6\right)}=\frac{6x\left(x+6\right)}{6x\left(x+6\right)}+\frac{x\left(x+6\right)}{6x\left(x+6\right)}+\frac{6x\left(120-x\right)}{6x\left(x+6\right)}\)
\(\Rightarrow720x+4320=6x^2+36x+x^2+6x+720x-6x^2\)
\(\Leftrightarrow6x^2+36x+x^2+6x+720x-6x^2-720x-4320=0\)
\(\Leftrightarrow x^2+42x-4320=0\)
\(\Leftrightarrow x^2+90x-48x-4320=0\)
\(\Leftrightarrow\left(x+90\right)\left(x-48\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+90=0\\x-48=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-90\\x=48\end{matrix}\right.\) ( tm )
\(ĐKXĐ:\hept{\begin{cases}x\ne0\\x\ne30\\x\ne24\end{cases}}\)
Ta có \(\frac{60}{\frac{120}{x}-4}+\frac{60}{\frac{120}{x}-5}=x\)
\(\Leftrightarrow\frac{60}{\frac{120-4x}{x}}+\frac{60}{\frac{120-5x}{x}}=x\)
\(\Leftrightarrow\frac{60x}{120-4x}+\frac{60x}{120-5x}=x\)
\(\Leftrightarrow\frac{60}{120-4x}+\frac{60}{120-5x}=1\left(Do\text{ }x\ne0\right)\)
\(\Leftrightarrow\frac{15}{30-x}=1-\frac{12}{24-x}\)
\(\Leftrightarrow\frac{15}{30-x}=\frac{24-x-12}{24-x}\)
\(\Leftrightarrow\frac{15}{30-x}=\frac{12-x}{24-x}\)
\(\Leftrightarrow360-15x=\left(12-x\right)\left(30-x\right)\)
\(\Leftrightarrow360-15x=360-42x+x^2\)
\(\Leftrightarrow x^2-27x=0\)
\(\Leftrightarrow x\left(x-27\right)=0\)
\(\Leftrightarrow x=27\left(Tm\text{ }ĐKXĐ\right)\)