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Question Number 138980 by 7770 last updated on 20/Apr/21

$$\sqrt{\frac{7x+2}{x+2}}-\frac{12}{7(7x+2)}=\frac{53}{28}$$$$findx$$

Answered by MJS_new last updated on 21/Apr/21

$$t=\sqrt{\frac{x+2}{7x+2}}>0\iff x=-\frac{2(t^2-1)}{7t^2-1}$$$$\frac{1}{t}-\frac{7t^2-1}{7}=\frac{53}{28}$$$$t^3+\frac{7}{4}t-1=0$$$$(t-\frac{1}{2})(t^2+\frac{1}{2}t+2)=0$$$$t=\frac{1}{2}$$$$x=2$$

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