Question

Giải pt

\(\frac{60}{x}=\frac{30}{x-6}+\frac{30}{x+10}\)

Answer 1

\(\frac{60}{x}=\frac{30}{x-6}+\frac{30}{x+10}\)

\(\Leftrightarrow\frac{60}{x}=\frac{30}{x-6}+\frac{30}{x+10},Đkxđ:x\ne0,6,-10\)

\(\Leftrightarrow\frac{60}{x}-\frac{30}{x-6}-\frac{30}{x+10}=0\)

\(\Leftrightarrow\frac{60\left(x-6\right)\left(x+10\right)-30x\left(x+10\right)=30\left(x-6\right)}{x\left(x-6\right)\left(x+10\right)}\)

\(\Leftrightarrow\frac{\left(60x-360\right)\left(x+10\right)-30x^2-300x-30x^2+180x}{x\left(x-6\right)\left(x+10\right)}\)

\(\Leftrightarrow\frac{60x^2+600x-360x-3600-30x^2-300x-30x^2+180}{x\left(x-6\right)\left(x=10\right)}=0\)

\(\Leftrightarrow\frac{120x-3600}{x\left(x-6\right)\left(x+10\right)}=0\)

\(\Leftrightarrow120x-3600=0\)

\(\Leftrightarrow120x=3600\)

\(\Leftrightarrow x=30;x\ne0;x\ne6,x\ne-10\)