Question

The equation $x-\frac{8}{|x-3|}=3-\frac{8}{|x-3|}$ has

• A. only one solution
• B. infinite solutions
• C. no solution
• D. two solutions

Answer 1

The correct option is C no solution

$x-\frac{8}{|x-3|}=3-\frac{8}{|x-3|}$

$\frac{x|x-3|-8}{|x-3|}=\frac{3|x-3|-8}{|x-3|}$

$x|x-3|-8=3|x-3|-8$

$\frac{|x-3|}{|x-3|}=\frac{3}{x}$

$1=\frac{3}{x},x=3$

when,$x=3,$

$3-\frac{8}{|3-3|}=3-\frac{8}{|3-3|}$$=\frac{1}{0}$

So there is no solution.