$$\frac{15}{x}+\frac{9x-7}{x+2} = 9$$

$$ \begin{aligned} \frac{15}{x}+\frac{9x-7}{x+2} &= 9&& \text{multiply ALL terms by } \color{blue}{ x(x+2) }. \\[1 em]x(x+2)\cdot\frac{15}{x}+x(x+2)\frac{9x-7}{x+2} &= x(x+2)\cdot9&& \text{cancel out the denominators} \\[1 em]15x+30+9x^2-7x &= 9x^2+18x&& \text{simplify left side} \\[1 em]9x^2+8x+30 &= 9x^2+18x&& \text{move all terms to the left hand side } \\[1 em]9x^2+8x+30-9x^2-18x &= 0&& \text{simplify left side} \\[1 em]9x^2+8x+30-9x^2-18x &= 0&& \\[1 em]-10x+30 &= 0&& \text{ move the constants to the right } \\[1 em]-10x &= -30&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{-30}{-10}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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