Question

СРОЧНО СРОЧНО СРОЧНО​

Answer 1

1.

$\frac{ {a}^{6} + {a}^{4} }{ {a}^{4} + {a}^{2} } = \frac{ {a}^{2} ( {a}^{4} + {a}^{2}) }{ {a}^{4} + {a}^{2} } = \frac{ {a}^{2} }{1} = {a}^{2}$

2.

$\frac{ {x}^{2} - 4x + 4 }{ {x}^{2} - 4 } = \frac{ {(x - 2)}^{2} }{(x - 2)(x + 2)} = \frac{(x - 2)(x - 2)}{(x - 2)(x + 2)} = \frac{x - 2}{x + 2}$

3.

$\frac{ {x}^{3} - 1 }{3 {x}^{2} + 3x + 3} = \frac{ {x}^{3} - {1}^{3} }{3( {x}^{2} + x + 1) } = \frac{(x - 1)( {x}^{2} + x + 1)}{3( {x}^{2} + x + 1)} = \frac{x - 1}{3}$

4.

$\frac{ {x}^{4} - {y}^{4} }{4 {x}^{2} + 4 {y}^{2} } = \frac{ {( {x}^{2} )}^{2} - {( {y}^{2} )}^{2} }{4( {x}^{2} + {y}^{2} )} = \frac{( {x}^{2} - {y}^{2} )( {x}^{2} + {y}^{2} )}{4( {x}^{2} + {y}^{2} )} = \frac{ {x}^{2} - {y}^{2} }{4}$

5.

$\frac{ax + ay - bx - by}{ax - ay - bx + by} = \frac{a(x + y) - b(x + y)}{a(x - y) - b(x - y)} = \frac{(x + y)(a - b)}{(x - y)(a - b)} = \frac{x + y}{x - y}$

6.

$\frac{ {(a + b)}^{2} - {c}^{2} }{a + b + c} = \frac{((a + b) - c)((a + b) + c)}{a + b + c} = \frac{(a + b - c)(a + b + c)}{a + b + c} = a + b - c$