Question

1. Разложите на множители х^2+25х+144=(х+...)×(х+...)
2. Сократите х^2-25/х^2+2х-35=х... .../х... ...
3. Сократите (х-5)^2/х^2+2х-35=х... .../х... ...
4. Сократите х+3/х^2+14х+33=.../...+...
5. Сократите 2х^2-10х+8/х^2-44=...×(х-...)/х^2+...х+...

Answer 1

1.

$x^2+25x+144=x^2+9x+16x+144=x(x+9)+16(x+9)=(x+9)(x+16)$

2.

$\frac{x^2-25}{x^2+2x-35}=\frac{(x-5)(x+5)}{x^2-5x+7x-35}=\frac{(x-5)(x+5)}{x(x-5)+7(x-5)}=\frac{(x-5)(x+5)}{(x-5)(x+7)}=\frac{x+5}{x+7}$

3.

$\frac{(х-5)^2}{x^2+2x-35}=\frac{(x-5)^2}{(x-5)(x+7)}=\frac{x-5}{x+7}$

4.

$\frac{х+3}{x^2+14x+33}=\frac{х+3}{x^2+3x+11x+33}=\frac{х+3}{x(x+3)+11(x+3)}==\frac{x+3}{(x+3)(x+11)}=\frac{1}{x+11}$

5. error?

$\frac{2х^2-10х+8}{х^2-44}=\frac{2(x^2-5x+4)}{(x-2\sqrt{11})(x+2\sqrt{11}}=\frac{2(x-1)(x-4)}{(x-2\sqrt{11})(x+2\sqrt{11}}$