Question

1=efetue as operações simplificando quando for possível 

a=3c/2x² . 4xy/9c³=
b=9/a²-4 . a+2/3x=
c=x²/xy-y² : x²+xy/x²-y²=
d=a²+2ab+b²/a²-b²=
e=2/b+4/12b=
f=1/x-3-3/x=
g=5/x²-9=

Answer 1

a=3c/2x² . 4xy/9c³=
$\frac{3c}{2x^2} . \frac{4xy}{9c^3} = \frac{3c}{9c^3} . \frac{4xy}{2x^2} = \frac{1}{3c^2}. \frac{2y}{x}= \frac{2y}{3c^2x}$

b=9/a²-4 . a+2/3x=
$\frac{9}{a^2-4} . \frac{a+2}{3x}= \frac{9}{3x} . \frac{a+2}{a^2-4}= \frac{3}{x} . \frac{1}{a-2}= \frac{3}{x(a-2)}$

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


d=a²+2ab+b²/a²-b²=
$\frac{a^2+2ab+b^2}{a^2-b^2}= \frac{(a+b)^2}{(a+b)(a-b)} = \frac{(a+b)}{(a-b)}$

e=2/b+4/12b=
$\frac{2}{b} + \frac{4}{12b}= \frac{2*12b+4*b}{12b^2} = \frac{24b+4b}{12b^2}=\frac{28b}{12b^2}= \frac{7}{3b}$

f=1/x-3-3/x=
$\frac{1}{x} -3- \frac{3}{x} =-3- \frac{2}{x}$

g=5/x²-9=
$\frac{5}{x^2} -9= \frac{5-9x^2}{x^2} = \frac{5}{x^2} - \frac{9x^2}{x^2}= \frac{5}{x^2} -9$

Concluímos que a letra g já está simplificada

Answer 2

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