Question

решите уравнения по алгебре ​

Answer 1

Объяснение:

1.

$\frac{3 {x}^{2} }{ {y}^{5} } \cdot \frac{y}{15x} = \frac{3}{15} \cdot {x}^{2 - 1 } \cdot {y}^{ 1 - 5 }= \\ = \frac{1}{5}x \cdot{y}^{ - 4} = \frac{x}{ 5{y}^{4} }$

2.

$\frac{ {x}^{2} - 25}{ {x}^{2} - 6x} \cdot \frac{ {x}^{2} - 12x + 36}{ {x}^{2} + 5x } = \\ = \frac{ ({x}- 5) \cancel{(x + 5)}}{ {x}\cancel{(x - 6)}} \cdot \frac{ {(x - 6)}^{\cancel{2 \: }} }{ {x} \cancel{(x + 5)}} = \\ = \frac{(x - 5)(x - 6)}{ {x}^{2} } = \frac{ {x}^{2} - 11x + 30}{ {x}^{2} }$

3.

$\frac{32 {b}^{5} }{15 {x}^{6} }: \frac{4 {b}^{3} }{45 {x}^{4} } = \frac{32 {b}^{5} }{15 {x}^{6} } \cdot\frac{45 {x}^{4} } {4 {b}^{3} }= \\ = \frac {8 \cdot{ \cancel{4 \: }}\cdot{b}^{5}\cdot \cancel{15}\cdot{3} \cdot {x}^{4} } { \cancel{15} \cdot {x}^{6} \cdot \cancel{4 \: } \cdot{b}^{3}} = \\ = {8}\cdot{b}^{5 - 3}\cdot{3} \cdot {x}^{4 - 6} = \frac{24 {b}^{2} }{ {x}^{2} }$

4.

$\frac{ {a}^{2} - 4a }{36 {a}^{2} - 1} : \frac{ {a}^{4} - 64a }{36 {a}^{2} - 12a + 1 } = \\ = \frac{ {a}^{2} - 4a }{36 {a}^{2} - 1} \cdot \frac{36 {a}^{2} - 12a + 1 } { {a}^{4} - 64a } = \\ = \frac{a( {a}{-} 4) }{(6 {a} {-} 1)(6a {+ }1)} \cdot \frac{(6{a}- 1)^{2} } {a( {a}^{3} - 4^{3} ) } = \\ \small = \frac{ \cancel{a \: }\cancel{( {a}- 4)} (6{a}- 1)^{\cancel{ \: 2 \: }}}{\cancel{a \: }(\cancel{6 {a} {- }1})(6a {+ }1) (\cancel{a{ - }4})( {a}^{2} {+} 4a{ + }4^{2} ) } = \\ = \frac{6a - 1}{(6a + 1)( {a}^{2} + 4a + 16)}$