Question

Simplifique as frações algébricas please


a) a⁴ + 2a² +
........a⁴-1

b) ab + ac + 2b + 2c
........2ab + 2ac

c) y² - 100
....2y + 20

d) m³ + m² - m - 1
......m⁴ - 1

e) 3a² - 6ab + 3b²
.......3a - 3b

Answer 1

a)
$\frac{a^4+2a^2+1}{a^4-1} = \frac{(a^2+1)^2}{(a^2+1)(a^2-1)} = \frac{a^2+1}{a^2-1}$

b)
$\frac{ab+ac+2b+2c}{2ab+2ac} = \\ \\ \frac{a(b+c)+2(b+c)}{2a(b+c)} = \frac{(a+2)(b+c)}{2a(b+c)} = \frac{a+2}{2a}$

c)
$\frac{y^2-100}{2y+20} = \frac{(y+10)(y-10)}{2(y+10)} = \frac{y-10}{2}$

d)
$\frac{m^3+m^2-m-1}{m^4-1} = \\ \\ \frac{m^2(m+1)-1(m+1)}{(m^2+1)(m^2-1)} = \frac{(m^2-1)(m+1)}{(m^2+1)(m^2-1)} = \frac{m+1}{m^2+1}$

e)
$\frac{3a^2-6ab+3b^2}{3a-3b} = \frac{3(a^2-2ab+b^2)}{3(a-b)} = \frac{3(a-b)^2}{3(a-b)} =a-b$