What is 1/2 x^{1/2-1} ?

The solution to 1/2 x^{1/2-1} is 1/(2sqrt(x))

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simplify 1/2 x^{1/2-1}

simplify

\frac{1}{2} x^{\frac{1}{2} - 1}

\frac{1}{2 x}

Solution steps

\frac{1}{2} x^{\frac{1}{2} - 1}

\frac{1}{2} - 1 = - \frac{1}{2}

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

= \frac{1}{2} \cdot \frac{1}{x ^{\frac{1}{2}}}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 x ^{\frac{1}{2}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 x ^{\frac{1}{2}}}

Apply exponent rule:

a^{\frac{1}{2}} = a

x^{\frac{1}{2}} = x

= \frac{1}{2 x}

(a + 3) (a + 3)

(x - 1) \cdot (x - 1)

(x - 1) \cdot (x + 1)

3 + (- 8)

6 x^{2}