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    "$$x' = \\frac{x-vt}{\\sqrt{1 - (\\frac{v}{c})^{2}}}$$\n",
    "$$t' = \\frac{t-\\frac{v}{c^2}x}{\\sqrt{1 - (\\frac{v}{c})^{2}}}$$\n"
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    "$$x'+ct' = \\frac{x-vt}{\\sqrt{1 - (\\frac{v}{c})^{2}}} + c\\frac{t-\\frac{v}{c^2}x}{\\sqrt{1 - (\\frac{v}{c})^{2}}} = \\frac{1}{\\sqrt{1 - (\\frac{v}{c})^2}}\\Big(x(1-\\frac{v}{c}) + t(c-v)\\Big) = \\frac{1}{\\sqrt{1 - (\\frac{v}{c})^2}}\\Big((x+ct)(1-\\frac{v}{c})\\Big) = (x+ct)\\frac{1-\\frac{v}{c}}{\\sqrt{1 - (\\frac{v}{c})^2}} $$\n"
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