Question

Упростите Выражение:(a/c-c/a)•1/a-c

Answer 1

$( frac{a}{c} - frac{c}{a} )* frac{1}{a-c} = frac{a^{2}-c^{2}}{ac} *frac{1}{a-c} = frac{(a-c)(a+c)}{ac} *frac{1}{a-c} = frac{a+c}{ac}$

Answer 2

$( frac{a}{c} - frac{c}{a} )* frac{1}{a-c} = frac{a+c}{ac} \ 1) frac{a}{c} - frac{c}{a} = frac{a*a}{ac} - frac{c*c}{ac} = frac{ a^{2} }{ac} - frac{ c^{2} }{ac} = frac{ a^{2} - c^{2} }{ac} \ 2) frac{ a^{2} - c^{2} }{ac} * frac{1}{a-c} = frac{(a-c)(a+c)}{ac(a-c)} = frac{a+c}{ac}$