1.7E: Rational Expressions (Exercises)

For the following exercises, simplify the expression.

61. \(\frac{x^{2}-x-12}{x^{2}-8 x+16}\) 62. \(\frac{4 y^{2}-25}{4 y^{2}-20 y+25}\)
63. \(\frac{2 a^{2}-a-3}{2 a^{2}-6 a-8} \cdot \frac{5 a^{2}-19 a-4}{10 a^{2}-13 a-3}\)
64. \(\frac{d-4}{d^{2}-9} \cdot \frac{d-3}{d^{2}-16}\)
65. \(\frac{m^{2}+5 m+6}{2 m^{2}-5 m-3} \div \frac{2 m^{2}+3 m-9}{4 m^{2}-4 m-3}\)
66. \(\frac{4 d^{2}-7 d-2}{6 d^{2}-17 d+10} \div \frac{8 d^{2}+6 d+1}{6 d^{2}+7 d-10}\)
67. \(\frac{10}{x}+\frac{6}{y}\)
68. \(\frac{12}{a^{2}+2 a+1}-\frac{3}{a^{2}-1}\)
69. \(\frac{\frac{1}{d}+\frac{2}{c}}{\frac{6 c+12 d}{d c}}\)
70. \(\frac{\frac{3}{x}-\frac{7}{y}}{\frac{2}{x}}\)