(9) \( \frac{4 m-9 n}{16 m^{2}}-\frac{9 n^{2}+1}{4 m-3 n} \)

Calculate or simplify the expression \( (4m-9n)/(16m^2)-(9n^2+1)/(4m-3n) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(4m-9n\right)}{16m^{2}}-\frac{\left(9n^{2}+1\right)}{\left(4m-3n\right)}\) - step1: Remove the parentheses: \(\frac{4m-9n}{16m^{2}}-\frac{9n^{2}+1}{4m-3n}\) - step2: Reduce fractions to a common denominator: \(\frac{\left(4m-9n\right)\left(4m-3n\right)}{16m^{2}\left(4m-3n\right)}-\frac{\left(9n^{2}+1\right)\times 16m^{2}}{\left(4m-3n\right)\times 16m^{2}}\) - step3: Reorder the terms: \(\frac{\left(4m-9n\right)\left(4m-3n\right)}{16m^{2}\left(4m-3n\right)}-\frac{\left(9n^{2}+1\right)\times 16m^{2}}{16\left(4m-3n\right)m^{2}}\) - step4: Rewrite the expression: \(\frac{\left(4m-9n\right)\left(4m-3n\right)}{16m^{2}\left(4m-3n\right)}-\frac{\left(9n^{2}+1\right)\times 16m^{2}}{16m^{2}\left(4m-3n\right)}\) - step5: Transform the expression: \(\frac{\left(4m-9n\right)\left(4m-3n\right)-\left(9n^{2}+1\right)\times 16m^{2}}{16m^{2}\left(4m-3n\right)}\) - step6: Multiply the terms: \(\frac{16m^{2}-48mn+27n^{2}-\left(9n^{2}+1\right)\times 16m^{2}}{16m^{2}\left(4m-3n\right)}\) - step7: Multiply the terms: \(\frac{16m^{2}-48mn+27n^{2}-\left(144n^{2}m^{2}+16m^{2}\right)}{16m^{2}\left(4m-3n\right)}\) - step8: Calculate: \(\frac{-48mn+27n^{2}-144n^{2}m^{2}}{16m^{2}\left(4m-3n\right)}\) - step9: Simplify: \(\frac{-48mn+27n^{2}-144n^{2}m^{2}}{\left(4m-3n\right)\times 16m^{2}}\) - step10: Multiply the terms: \(\frac{-48mn+27n^{2}-144n^{2}m^{2}}{64m^{3}-48nm^{2}}\) The simplified expression is \( \frac{-48mn+27n^{2}-144n^{2}m^{2}}{64m^{3}-48nm^{2}} \).