Question

Помогите пожалуйста по алгебре

Answer 1

$2)$
$\frac{ x^{2} -3}{ x^{2} -1} \ \textgreater \ 1$
$\frac{ x^{2} -3}{ x^{2} -1} -1\ \textgreater \ 0$
$\frac{ x^{2} -3-x^2+1}{ x^{2} -1} \ \textgreater \ 0$
$\frac{-2}{(x-1)(x+1)} \ \textgreater \ 0$
$\frac{2}{(x-1)(x+1)} \ \textless \ 0$
$(x-1)(x+1)\ \textless \ 0$

-----+-----(-1)------_------(1)-----+---------
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Ответ: $(-1;1)$

$4)$
$\frac{ x^{2} +7x-78}{x^2-9} \geq 5$
$\frac{ x^{2} +7x-78}{x^2-9}-5 \geq 0$
$\frac{ x^{2} +7x-78-5x^2+45}{x^2-9} \geq 0$
$\frac{ -4x^{2} +7x-33}{x^2-9} \geq 0$
$\frac{ 4x^{2} -7x+33}{x^2-9} \leq 0$
$\frac{ 4x^{2} -7x+33}{(x-3)(x+3)} \leq 0$
$4x^{2} -7x+33=0$
$D=(-7)^2-4*4*33\ \textless \ 0$
$(x-3)(x+3)\ \textless \ 0$
-----+-----(-3)------_------(3)-----+---------
                 ////////////////////
Ответ: $(-3;3)$