Question

F (x)= 5x-14 G (x)= 12x+8 H (x)= 62x-54 Dadas las funciones resolver las siguientes operaciones a. F (x)+ G (x) b. G (x)- (H (x)-F (x)) c. (G (x)-F (x)) (H (x)+G (x) d. (F (x)-H (x))/ (G (x)+ F(x) e. G (x) / H (x9

Answer 1

Answer:

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

Step-by-step 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) $\frac{f(x)-h(x)}{g(x) + f(x) }$

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

$\frac{-57\cdot x +40}{17\cdot x -6}$

e) $\frac{g(x)}{h(x)}$

$\frac{12\cdot x + 8}{62\cdot x - 54}$

$\frac{4\cdot (3\cdot x +2)}{2\cdot (31\cdot x -27)}$

$2\cdot \left(\frac{3\cdot x + 2}{31\cdot x - 27} \right)$