How do I solve this 3 x 3 system of non-linear equations?

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I have to solve this problem, but I am stucked

$$y1 = \frac{x1}{x1 + x2} $$

$$y2 = \frac{x1 +x2}{x1 + x2 +x3} $$

$$y3 = {x1 + x2 +x3} $$

How do I solve for x1, x2, and x3?

The best I coud do is

$$y2y3 = {x1 +x2} $$

In this part I am stucked, how do I get the x1?

The answer is $$x1 = {y1y2y3} $$ $$x2 = {y2y3}-{y1y2y3} $$ $$x3 = {y3}-{y2y3} $$

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$$y_2 = \frac{x_1 +x_2}{x_1 + x_2 +x_3}= \frac{x_1 +x_2}{y_3}$$

$$y_1 = \frac{x_1}{x_1 + x_2}= \frac{x_1}{y_2y_3}$$