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Guerric P · Answer 1 · 2022-05-12T08:33:11+0000

Answer:

a)
$17\cdot x -6$ , b)
$-45\cdot x +48$ , c)
$518\cdot x^(2) +1306\cdot x -1012$ , d)
$(-57\cdot x +40)/(17\cdot x -6)$ , e)
$2\cdot \left((3\cdot x + 2)/(31\cdot x - 27) \right)$

Explanation:

Sean
$f(x) = 5\cdot x -14$ ,
$g(x) = 12\cdot x + 8$ y
$h(x) = 62\cdot x - 54$ . A continuación, desarrollamos las siguientes operaciones:

a)
f(x) + g(x)

$(5\cdot x - 14) + (12\cdot x + 8)$

$17\cdot x -6$

b)
g(x) - [h(x)-f(x)]

$(12\cdot x + 8) - [(62\cdot x - 54)-(5\cdot x - 14)]$

$12\cdot x + 8 - (57\cdot x -40)$

$12\cdot x +8 -57\cdot x +40$

$-45\cdot x +48$

c)
$[g(x)-f(x)]\cdot [h(x)+g(x)]$

$[(12\cdot x + 8)-(5\cdot x -14)]\cdot [(62\cdot x -54)+(12\cdot x +8)]$

$(12\cdot x +8 -5\cdot x +14) \cdot (62\cdot x -54+12\cdot x+8)$

$(7\cdot x +22)\cdot (74\cdot x-46)$

$7\cdot x \cdot (74\cdot x - 46)+22\cdot (74\cdot x -46)$

$(7\cdot x)\cdot (74\cdot x) - 46\cdot (7\cdot x )+22\cdot (74\cdot x)-22\cdot (46)$

$518\cdot x^(2)-322\cdot x +1628\cdot x -1012$

$518\cdot x^(2) +1306\cdot x -1012$

d)
(f(x)-h(x))/(g(x) + f(x) )

$((5\cdot x - 14)-(62\cdot x - 54))/((12\cdot x +8)+(5\cdot x -14))$

$(-57\cdot x +40)/(17\cdot x -6)$

e)
(g(x))/(h(x))

$(12\cdot x + 8)/(62\cdot x - 54)$

$(4\cdot (3\cdot x +2))/(2\cdot (31\cdot x -27))$

$2\cdot \left((3\cdot x + 2)/(31\cdot x - 27) \right)$

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