1. **State the problem:** We are given two functions: $$k(x) = \frac{6x+5}{7x-9}$$ $$h(x) = \frac{5x-2}{9x+1}$$ We need to find the composition $kh$, which means $k(h(x))$. 2. **Recall the composition formula:** $$kh(x) = k(h(x)) = k\left(\frac{5x-2}{9x+1}\right)$$ This means we substitute $h(x)$ into every $x$ in $k(x)$. 3. **Substitute $h(x)$ into $k(x)$:** $$k\left(\frac{5x-2}{9x+1}\right) = \frac{6\left(\frac{5x-2}{9x+1}\right) + 5}{7\left(\frac{5x-2}{9x+1}\right) - 9}$$ 4. **Simplify numerator:** $$6\left(\frac{5x-2}{9x+1}\right) + 5 = \frac{6(5x-2)}{9x+1} + \frac{5(9x+1)}{9x+1} = \frac{30x - 12 + 45x + 5}{9x+1} = \frac{75x - 7}{9x+1}$$ 5. **Simplify denominator:** $$7\left(\frac{5x-2}{9x+1}\right) - 9 = \frac{7(5x-2)}{9x+1} - \frac{9(9x+1)}{9x+1} = \frac{35x - 14 - 81x - 9}{9x+1} = \frac{-46x - 23}{9x+1}$$ 6. **Write the full expression:** $$k(h(x)) = \frac{\frac{75x - 7}{9x+1}}{\frac{-46x - 23}{9x+1}}$$ 7. **Divide the fractions:** $$k(h(x)) = \frac{75x - 7}{9x+1} \times \frac{9x+1}{-46x - 23}$$ 8. **Cancel common factor $9x+1$:** $$k(h(x)) = \frac{75x - 7}{\cancel{9x+1}} \times \frac{\cancel{9x+1}}{-46x - 23} = \frac{75x - 7}{-46x - 23}$$ 9. **Final answer:** $$\boxed{k(h(x)) = \frac{75x - 7}{-46x - 23}}$$ This is the composition of $k$ and $h$.