i just need someone to show me maybe one example of how to solve a problem like
x+5/x+3=8
or
1+1/x=6/x^2
Can anyone help please?
1) $\displaystyle x\ne 0$ so the equation is $\displaystyle x+\frac 5x +3=8\leftrightarrow x^2+5+3x=8x\leftrightarrow$$\displaystyle x^2-5x+5=0\rightarrow x_{1,2}=\frac {-(-5)\pm\sqrt{5^2-4\cdot 1\cdot 5}}{2\cdot 1}=\frac {5\pm\sqrt{25-20}}{2}=\frac {5\pm\sqrt{5}}2$
2) $\displaystyle x\ne 0$ so the equation is $\displaystyle 1+\frac 1x=\frac 6{x^2}\leftrightarrow x^2+x=6\leftrightarrow x^2+x-6=0\leftrightarrow (x+3)(x-2)=0\rightarrow x=-3\,\text{or}\,2$