====== Macejova Matika ======
===== Nerovnice =====
//a//
$$(4 - 5x) * 2 - 7(x + 4) + 2x <= 0$$
$$8 - 10x - 7x - 28 + 2x <= 0$$
$$-15x - 20 <= 0$$
$$-15x <= 20$$
$$-3x <= 4$$
$$x <= -4/3$$
----
//d//

<m>2*{{4x-5}/3}-{5x}/2>={x+1}/6</m>

<m>{8x-10}/3-{5x}/2>={x+1}/6</m>

<m>16x-20-15x>=x+1</m>

<m>x-20>=x+1</m>

<m>-20>=1</m>

Nerovnice nemá řešení
----
//g//

<m>4/7x-(8-x)^2/14+{x^2/2}*7^-1+(-2)^2<0</m>

<m>{4x}/7-{64-16x+x^2}/14+{x^2/2}*{1/7}+4<0</m>

<m>{8x}/14+{-64+16x-x^2}/14+{x^2/14}<-4</m>

<m>8x-64+16x-x^2+x^2<-56</m>

<m>24x-64<-56</m>

<m>24x<8</m>

<m>x<8/24</m>

<m>x<1/3</m>

===== Rovnice s neznámou ve jmenovateli =====
==== Zadání ====
<m>{3x+7}/{x-5}-{{5+x}/{x}}*3-{25-3x}/{x^2-5x}=0</m>

=== Podmínky ===
<m>x<>5</m>
<m>x<>0</m>

=== Řešení ===
<m>{3x+7}/{x-5}-{15+3x}/{x}-{25-3x}/{x^2-5x}=0</m>

<m>{3x^2+7x-(15+3x)(x-5)}/{x^2-5x}={25-3x}/{x^2-5x}</m>

<m>{3x^2+7x-15x+75-3x^2+15x}/{x^2-5x}={25-3x}/{x^2-5x}</m>

<m>{7x+75}/{x^2-5x}={25-3x}/{x^2-5x}</m>

<m>7x+75=25-3x</m>

<m>10x=-50</m>

=== Výsledek ===
<m>x=-5</m>

==== Zadání ====
<m>{6-z}/{1+z}-{2(4z-3)}/{z^2-1}=z/{1-z}</m>

=== Podmínky ===
<m>z<>pm 1</m>

=== Řešení ===
<m>{6-z}/{1+z}-{8z-6}/{z^2-1}=z/{1-z}</m>

<m>{6-z}/{1+z}-z/{1-z}={8z-6}/{z^2-1}</m>

<m>{(6-z)(1-z)-z(1+z)}/{1-z^2}={8z-6}/{z^2-1}</m>

<m>{6-6z-z+z^2-z-z^2}/{1-z^2}={8z-6}/{z^2-1}</m>

<m>{-8z+6}/{1-z^2}={-8z+6}/{1-z^2}</m>

=== Výsledek ===
<m>z in bbR-delim{lbrace}{pm 1}{rbrace}</m>