Объяснение:

1.

1)

[tex] \frac{ - 96 {a}^{2} {b}^{10} {c}^{7} }{ - 4 {a}^{2} {b}^{7} {c}^{6} } = 24 {b}^{3}c [/tex]

2)

[tex] \frac{(2c {x}^{3} {y}^{5} ) {}^{5} }{10 {c}^{5} {x}^{10} {y}^{10} } = \frac{ {2}^{5} {c}^{5} {x}^{15} {y}^{25} }{10 {c}^{5} {x}^{10} {y}^{10} } = \frac{16 \times 2 {x}^{5} {y}^{15} }{10} = \frac{16 {x}^{5} {y}^{15} }{5} [/tex]

3)

[tex] \frac{36 {a}^{2} {b}^{3} - 24 {a}^{5} {b}^{4} + 16 {a}^{7} {b}^{3} }{4 {a}^{2} {b}^{3} } = \frac{4 {a}^{2} {b}^{3} (9 - 6 {a}^{3} b + 4 {a}^{5} )}{4 {a}^{2} {b}^{3} } = 9 - 6 {a}^{3} b + 4 {a}^{4} [/tex]

4)

[tex] \frac{7x {y}^{5} {z}^{6} - 9 {x}^{2} {y}^{3} {z}^{5} + 5 {x}^{5} {y}^{4} {z}^{3} }{5x {y}^{3} {z}^{3} } = \frac{x {y}^{3} {z}^{3}(7 {y}^{2} {z}^{3} - 9x {z}^{2} + 5 {x}^{4}y) }{5x {y}^{3} {z}^{3} } = \frac{7 {y}^{2} {z}^{3} - 9x {z}^{2} + 5 {x}^{4} y}{5} [/tex]

5)

[tex] \frac{2a {b}^{2} - 3 {a}^{3} {b}^{4} + 4a {b}^{7} }{2a {b}^{2} } = \frac{a {b}^{2}(2 - 3 {a}^{2} {b}^{2} + 4 {b}^{5} )}{2a {b}^{2} } = \frac{2 - 3 {a}^{2} {b}^{2} + 4 {b}^{5} }{2} = 1 - \frac{3 {a }^{2} {b}^{2} }{2} + 2 {b}^{5}[/tex]

2.

1)

[tex]3ab - 4 {a}^{2} bc + 9abc = ab(3 - 4ac + 9c)[/tex]

2)

[tex]14 {x}^{2} {y}^{5} + 42 {x}^{3} {y}^{4} - 21 {x}^{2} {y}^{3} = 7 {x}^{2} {y}^{3}(2 {y}^{2} + 6xy - 3)[/tex]

3)

[tex]15a(x - y) - 2b(x - y ) = (x - y)(15a - 2b)[/tex]

4)

[tex]4ab {c}^{5} + 2ab - 6abc = 2ab(2 {c}^{5} + 1 - 3c)[/tex]

5)

[tex](x - 7) + 2b(x - 7) = (x - 7)(1 + 2b)[/tex]