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Popular Algebra >

expand ((2sqrt(x)+1)/(4sqrt(x)))*((-16)/(sqrt(x)(1+\sqrt{x))(x-4)^2})

Solution

expand

(\frac{2 x + 1}{4 x}) \cdot (\frac{- 16}{x ( 1 + x ) ( x - 4 ) ^{2}})

Solution

- \frac{8 x + 4}{x ^{3} x + x ^{3} - 8 x ^{2} x + 16 x x - 8 x ^{2} + 16 x}

Solution steps

(\frac{2 x + 1}{4 x}) (\frac{- 16}{x ( 1 + x ) ( x - 4 ) ^{2}})

Remove parentheses:

(a) = a

= \frac{2 x + 1}{4 x} \cdot \frac{- 16}{x ( 1 + x ) ( x - 4 ) ^{2}}

\frac{- 16}{x ( 1 + x ) ( x - 4 ) ^{2}} = - \frac{16}{x ^{2} x - 8 x x + 16 x + x ^{3} - 8 x ^{2} + 16 x}

= \frac{2 x + 1}{4 x} (- \frac{16}{x ^{3} + x ^{2} x - 8 x ^{2} + 16 x - 8 x x + 16 x})

Remove parentheses:

(- a) = - a

= - \frac{2 x + 1}{4 x} \cdot \frac{16}{x ^{2} x - 8 x x + 16 x + x ^{3} - 8 x ^{2} + 16 x}

Multiply fractions:

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

= - \frac{( 2 x + 1 ) \cdot 16}{4 x ( x ^{2} x - 8 x x + 16 x + x ^{3} - 8 x ^{2} + 16 x )}

Divide the numbers:

\frac{16}{4} = 4

= - \frac{4 ( 2 x + 1 )}{x ( x ^{3} + x ^{2} x - 8 x ^{2} + 16 x - 8 x x + 16 x )}

Expand

x (x^{3} + x^{2} x - 8 x^{2} + 16 x - 8 x x + 16 x) : x^{3} x + x^{3} - 8 x^{2} x + 16 x x - 8 x^{2} + 16 x

= - \frac{4 ( 2 x + 1 )}{x ^{3} x + x ^{3} - 8 x ^{2} x - 8 x ^{2} + 16 x x + 16 x}

Expand

4 (2 x + 1) : 8 x + 4

= - \frac{8 x + 4}{x ^{3} x + x ^{3} - 8 x ^{2} x - 8 x ^{2} + 16 x x + 16 x}

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