Question

3. Combine e simplifique
a b
(a) −
b a
3 1
(b) x −2 + 2−x
1
(c)
(d) xy2+ x y
4a b
(e) + 4a b

Answer 1

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

$\frac{3}{x-2}+\frac{1}{2-x}=\frac{3(2-x)+1(x-2)}{-x^2+4x-4}=\frac{6-3x+x-2}{-x^2+4x-4}=\frac{-2x+4}{-x^2+4x-4}$

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

$\frac{x}{xy^2}+\frac{y}{x^2y}=\frac{x*x+y*y}{x^2y^2}=\frac{x^2+y^2}{x^2y^2}$

$\frac{4a}{b}+\frac{b}{4a} = \frac{4a*b+b*4a}{4ab}=\frac{8ab}{4ab}=2$