Racionalize as frações:
a) 1/✓x
b) 2/✓x+✓4
c) 3/1-✓x
d) 4/✓x^3
Soluções para a tarefa
Resposta:
\frac{1}{ \sqrt{x} } = \frac{1}{ \sqrt{x} } \times \frac{ \sqrt{x} }{ \sqrt{x} } = \boxed{\frac{ \sqrt{x} }{x}}
x
1
=
x
1
×
x
x
=
x
x
B)
\begin{lgathered}\frac{2}{ \sqrt{x} + \sqrt{4} } = \frac{2}{ \sqrt{x} + 2} = \frac{2}{ \sqrt{x} + 2} \times \frac{( \sqrt{x } - 2)}{ (\sqrt{x} - 2 )} = \\ \frac{2( \sqrt{x} - 2) }{( \sqrt{x} + 2)( \sqrt{x} - 2) } = \boxed{\frac{2 \sqrt{x} - 4}{x - 4} }\end{lgathered}
x
+
4
2
=
x
+2
2
=
x
+2
2
×
(
x
−2)
(
x
−2)
=
(
x
+2)(
x
−2)
2(
x
−2)
=
x−4
2
x
−4
C)
\begin{lgathered}\frac{3}{1 - \sqrt{x} } = \frac{3}{1 - \sqrt{x} } \times \frac{(1 + \sqrt{x} )}{(1 + \sqrt{x} )} = \\ \frac{3(1 + \sqrt{x} )}{(1 - \sqrt{x} )(1 + \sqrt{x} )} = \boxed{\frac{3 + 3 \sqrt{x} }{1 - x}}\end{lgathered}
1−
x
3
=
1−
x
3
×
(1+
x
)
(1+
x
)
=
(1−
x
)(1+
x
)
3(1+
x
)
=
1−x
3+3
x
D)
\begin{lgathered}\frac{4}{ \sqrt{ {x}^{3} } } = \frac{4}{x \sqrt{x} } = \frac{4}{x \sqrt{x} } \times \frac{ \sqrt{x} }{ \sqrt{x} } = \\ \frac{4 \sqrt{x} }{x \times x} = \boxed{\frac{4 \sqrt{x} }{ {x}^{2} }}\end{lgathered}
x
3
4
=
x
x
4
=
x
x
4
×
x
x
=
x×x
4
x
=
x
2
4
x
Explicação passo-a-passo:
espero ter ajudado