$$\frac{x+5}{x}=\frac{x-7}{x-2}$$
$x=1$
$$\left(x-2\right)\left(x+5\right)=x\left(x-7\right)$$
$$x^{2}+3x-10=x\left(x-7\right)$$
$$x^{2}+3x-10=x^{2}-7x$$
$$x^{2}+3x-10-x^{2}=-7x$$
$$3x-10=-7x$$
$$3x-10+7x=0$$
$$10x-10=0$$
$$10x=10$$
$$x=\frac{10}{10}$$
$$x=1$$
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