Question

поможіть будь ласочка ​

Answer 1

5. а)

$\frac{b}{a - b} + \frac{a}{a + b}$

$\frac{b \times (a + b) + a \times (a - b)}{(a - b) \times (a + b)}$

$\frac{ab + {b}^{2} + {a}^{2} - ab }{ {a}^{2} - {b}^{2} }$

$\frac{ {b}^{2} + {a}^{2} }{ {a}^{2} - {b}^{2} }$

б)

$\frac{15x + y}{ {x}^{2} - {y}^{2} } + \frac{11}{x - y}$

$\frac{15x + y}{(x - y) \times (x \times y)} + \frac{11}{x - y}$

$\frac{15x + y + 11(x + y)}{(x - y) \times (x + y)}$

$\frac{15x + y + 11x + 11y}{ {x}^{2} - {y}^{2} }$

$\frac{26x + 12y}{ {x}^{2} - {y}^{2} }$

в)

$\frac{x}{ {x}^{2} - 25} - \frac{x - 8}{ {x}^{2} - 10x + 25}$

$\frac{x}{(x - 5)(x + 5)} - \frac{x - 8}{ {(x - 5)}^{2} }$

$\frac{x \times ( x - 5) - (x + 5) \times (x - 8)}{ {(x + 5) \times (x - 5)}^{2} }$

$\frac{ {x}^{2} - 5x - ( {x}^{2} - 8x + 5x - 40) }{(x + 5) \times ( {x}^{2} - 10x + 25) }$

$\frac{ {x}^{2} - 5x - ( {x}^{2} - 3x - 40)}{ {x}^{3} - 10 {x}^{2} + 25x + 5 {x}^{2} - 50x + 125 }$

$\frac{ {x}^{2} - 5x - {x}^{2} + 3x + 40 }{ {x}^{3} - 5 {x}^{2} - 25x + 125}$

$\frac{ - 2x + 40}{ {x}^{3} - 5 {x}^{2} - 25x + 125}$

6.

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

$\frac{ {x}^{2} + 2xy + {y}^{2} + {x}^{2} - 2xy + {y}^{2} }{ {x}^{2} - {y}^{2} }$

$\frac{2 {x}^{2} + 2 {y}^{2} }{ {x}^{2} - {y}^{2} }$

тотожність доведена