Složený lomený výraz

$\Huge \frac{\frac{b}{a^2+ab} + \frac{2}{a+b}+\frac{a}{b^2+ab}}{\frac{a^2-b^2}{4ab}}= \frac{\frac{b}{a(a+b)} + \frac{2}{a+b}+\frac{a}{b(a+b)}}{\frac{(a-b)(a+b)}{4ab}}=\frac{\frac{b^2+2ab+a^2}{ab(a+b)}}{\frac{(a-b)(a+b)}{4ab}}=$

$\huge =\frac{(a+b)^2}{ab(a+b)} \times \frac{4ab}{(a-b)(a+b)}=\frac{4}{a-b}$

$a \neq 0 $

$b \neq 0 $

$a \neq \pm b $

$\Huge \frac{\frac{x}{x-2}-2}{\frac{16-x^2}{x^2-4x+4}}=\frac{\frac{x-2(x-2)}{x-2}}{\frac{(4-x)(4+x)}{(x-2)^2}}=\frac{\frac{x-2x+4}{x-2}}{\frac{(4-x)(4+x)}{(x-2)^2}}=$

$\huge =\frac{x-2x+4}{x-2} \times \frac{(r-2)^2}{(4-x)(4+x)}=\frac{(x-2)(x-2x+4)}{(4-x)(4+x)}=$

$\huge = \frac{x^2-2x^2+4x-2x+4x-8}{(4-x)(4+x)}=\frac{-x^2+6x-8}{(4-x)(4+x)}=$

$\huge =\frac{-(x^2-6x+8)}{(4-x)(4+x)}=\frac{-(x-4)(x-2)}{-(x-4)(4+x)}=\frac{x-2}{x+4}$

$x \neq 2 $

$x \neq \pm 4 $

$\Huge \frac{\frac{2a}{a+2}+\frac{6a}{6-3a}+\frac{8a}{a^2-4}}{\frac{a-4}{a-2}}=\frac{\frac{2a}{a+2}-\frac{6a}{3(a-2)}+\frac{8a}{a^2-4}}{\frac{a-4}{a-2}}=$

$\Huge =\frac{\frac{6a(a-2)-6a(a+2)+24a}{3(a-2)(a+2)}}{\frac{a-4}{a-2}}=\frac{\frac{6a^2-12a-6a^2-12a+24a}{3(a-2)(a+2)}}{\frac{a-4}{a-2}}=0$

$a \neq 4 $

$a \neq \pm 2 $

$\Huge \frac{(\frac{2-3(x+2)}{x+2})(\frac{2-x+x-1}{2-x})}{\frac{3(3x+4)}{x(x^2-4)}}=\frac{(\frac{2-3x-6}{x+2})(\frac{1}{2-x})}{\frac{3(3x+4)}{x(x-2)(x+2)}}=$

$\Huge =\frac{(\frac{-3x-4}{x+2})(\frac{1}{2-x})}{\frac{3(3x+4)}{x(x-2)(x+2)}}=\frac{-(3x+4)}{x+2} \times \frac{1}{2-x} \times \frac{x(x-2)(x+2)}{3(3x+4)}=$

$\huge =\frac{-x(x-2)}{3(2-x)}=\frac{x(2-x)}{3(2-x)}=\frac{x}{3}$

$x \neq 0$

$x \neq \pm 2$

$x \neq -\frac{4}{3}$