Question

Помогите, срочно, даю 50 баллов

Answer 1

Разложить на множители:

$x^2+5x-14 =\=left(x^2-2xright)+left(7x-14right)=\=xleft(x-2right)+7left(x-2right)=\=left(x-2right)left(x+7right)$

$5x^2+7x-24 =\= left(5x^2-8xright)+left(15x-24right) =\= xleft(5x-8right)+3left(5x-8right) =\= left(5x-8right)left(x+3right)$

$6x^2+5x-1 = \= (6x^2-x)+(6x-1) = \= x(6x-1)+1(6x-1) = \= (6x-1)(x+1)$

Сократить дробь:

$frac{x^2+7x+12}{x+4} = frac{left(x^2+3xright)+left(4x+12right)}{x+4}=\\= frac{xleft(x+3right)+4left(x+3right)}{x+4} = frac{left(x+3right)left(x+4right)}{x+4} = x+3$

$frac{3x^2-16x+5}{x-5}= frac{left(3x^2-xright)+left(-15x+5right)}{x-5} =\\frac{xleft(3x-1right)-5left(3x-1right)}{x-5} = frac{left(3x-1right)left(x-5right)}{x-5} = 3x-1$

$frac{3x^2+5x-2}{x^2-4} = frac{left(3x^2-xright)+left(6x-2right)}{left(x+2right)left(x-2right)} =\\ frac{xleft(3x-1right)+2left(3x-1right)}{left(x+2right)left(x-2right)} = frac{left(3x-1right)left(x+2right)}{left(x+2right)left(x-2right)} =frac{3x-1}{x-2}$