$$ \begin{aligned} -\frac{6}{5k+9} &= \frac{5}{3}&& \text{multiply ALL terms by } \color{blue}{ (5k+9)\cdot3 }. \\[1 em]-(5k+9)\cdot3\cdot\frac{6}{5k+9} &= (5k+9)\cdot3\cdot\frac{5}{3}&& \text{cancel out the denominators} \\[1 em]-18 &= 25k+45&& \text{ swap the left and right side of the equation } \\[1 em]25k+45 &= -18&& \text{ move 45 to the right } \\[1 em]25k &= -18-45&& \\[1 em]25k &= -63&& \text{ divide both sides by $ 25 $ } \\[1 em]k &= -\frac{63}{25}&& \\[1 em] \end{aligned} $$

This page was created using