Question

Me ajudem pelo amor de Deus-Efetue as operações indicadas em caso abaixo:
a)a-5/2a + 4/3a
b)x/2x + 2y-3x/x+y
c)a/b + b/a+b + a^2/a^2+ab
d)m+n/m-n + n-m/m+n - 4mn/m^2-n^2
e)x+2/x^2+x - x+1/x^2+2x+1 - 1/x

Answer 1

a Resposta da a e b estão na imagen

Answer 2

Oie, Td Bom?!

a)

$=\frac{a - 5}{2a} + \frac{4}{3a}$

$= \frac{3(a - 5)}{3 \: . \: 2a} + \frac{2 \: . \: 4}{2 \: . \: 3a}$

$= \frac{3(a - 5)}{6a} + \frac{8}{6a}$

$= \frac{3(a - 5) + 8}{6a}$

$= \frac{3a - 15 + 8}{6a}$

$= \frac{3a - 7 }{6a}$

b)

$= \frac{x}{2x} + \frac{2y - 3x}{x + y}$

$= \frac{1}{2} + \frac{2y + 3x}{x + y}$

$= \frac{(x + y) \: . \: 1}{(x + y) \: . \: 2} + \frac{2(2y - 3x)}{2(x + y)}$

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

$= \frac{x + y + 4y - 6x}{2x + 2y}$

$= \frac{ - 5x + 5y}{2x + 2y}$

c)

$= \frac{a}{b} + \frac{b}{a + b} + \frac{a {}^{2} }{a {}^{2} + ab}$

$= \frac{a}{b} + \frac{b}{a + b} + \frac{a {}^{2} }{a \: . \: (a + b)}$

$= \frac{a}{b} + \frac{b }{a + b} + \frac{a}{a + b}$

$= \frac{(a + b)a}{(a + b)b} + \frac{b \: . \: b}{b \: . \: (a + b) } + \frac{ba}{b \: . \: (a + b)}$

$= \frac{(a + b)a}{b \: . \: (a + b)} + \frac{b {}^{2} }{b \: . \: (a + b)} + \frac{ab}{b \: . \: (a + b)}$

$= \frac{a \: . \: (a + b) + b {}^{2} + ab}{b \: . \: (a + b)}$

$= \frac{a {}^{2} + ab + b {}^{2} + ab}{b \: . \: (a + b)}$

$= \frac{a {}^{2} + 2ab + b {}^{2} }{b \: . \: (a + b)}$

$= \frac{(a + b) {}^{2} }{b \: . \: (a + b)}$

$= \frac{a + b}{b}$

d)

$= \frac{m + n}{m - n} + \frac{n - m}{m + n} - \frac{4mn}{m {}^{2} - n {}^{2} }$

$= \frac{m + n}{m - n} + \frac{n - m}{m + n} - \frac{4mn}{(m - n) \: . \: (m + n)}$

$= \frac{(m + n) \: . \: (m + n)}{(m + n) \: . \: (m - n)} + \frac{(m - n) \: . \: (n - m)}{(m - n) \: . \: (m + n)} - \frac{4mn}{(m - n) \: . \: (m + n)}$

$= \frac{(m + n) {}^{2} }{(m - n) \: . \: (m + n)} + \frac{(m - n) \: . \: (n - m)}{(m - n) \: . \: (m + n)} - \frac{4mn}{(m - n) \: . \: (m + n)}$

$= \frac{(m + n) {}^{2} + (m - n) \: . \: (n - m) - 4mn }{(m - n) \: . \: (m + n)}$

$= \frac{(m + n) {}^{2} + (m - n) \: . \: ( - (m - n)) - 4mn }{(m - n) \: . \: (m + n)}$

$= \frac{(m + n) {}^{2} - (m - n) {}^{2} - 4mn}{(m - n) \: . \: (m + n)}$

$= \frac{2n \: . \: 2m - 4mn}{(m - n) \: . \: (m + n)}$

$= \frac{4mn - 4mn}{(m - n) \: . \: (m + n)}$

$= \frac{0}{(m - n) \: . \: (m + n)}$

$= 0$

e)

$= \frac{x + 2}{x {}^{2} + x} - \frac{x + 1}{x {}^{2} + 2x + 1} - \frac{1}{x}$

$= \frac{x + 2}{x \: . \: (x + 1)} - \frac{x + 1}{(x + 1) {}^{2} } - \frac{1}{x}$

$= \frac{x + 2}{x \: . \: (x + 1)} - \frac{1}{x + 1} - \frac{1}{x}$

$= \frac{x +2 }{x \:. \: (x + 1) } - \frac{x \: . \: 1}{x \: . \: (x + 1)} - \frac{(x + 1) \: . \: 1}{(x + 1) \: . \: x}$

$= \frac{x + 2}{x \: . \: (x + 1)} - \frac{x}{x \: . \: (x + 1)} - \frac{x + 1}{x \: . \: (x + 1)}$

$= \frac{x + 2 -x - (x + 1)}{x \: . \: (x + 1)}$

$= \frac{2 - (x + 1)}{x \: . \: (x + 1)}$

$= \frac{2 - x - 1}{x {}^{2} + x }$

$= \frac{1 - x}{x {}^{2} + x}$

Att. Makaveli1996