Question
$$2 \cdot \frac{x}{3}+5\frac{x^2}{x}+3 = 2 \cdot \frac{x}{3}+5\frac{x^2}{x}+3$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 2 \cdot \frac{x}{3}+5\frac{x^2}{x}+3 &= 2 \cdot \frac{x}{3}+5\frac{x^2}{x}+3&& \text{multiply ALL terms by } \color{blue}{ 3x }. \\[1 em]3x\cdot2 \cdot \frac{x}{3}+3x\cdot5\frac{x^2}{x}+3x\cdot3 &= 3x\cdot2 \cdot \frac{x}{3}+3x\cdot5\frac{x^2}{x}+3x\cdot3&& \text{cancel out the denominators} \\[1 em]2x^2+15+9x &= 2x^2+15+9x&& \text{simplify left and right hand side} \\[1 em]2x^2+9x+15 &= 2x^2+9x+15&& \text{move all terms to the left hand side } \\[1 em]2x^2+9x+15-2x^2-9x-15 &= 0&& \text{simplify left side} \\[1 em]2x^2+9x+15-2x^2-9x-15 &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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