What is (x+2)/(4x^2+5x+1)*(4x+1)/(x^2-4) ?

The solution to (x+2)/(4x^2+5x+1)*(4x+1)/(x^2-4) is 1/((x+1)(x-2))

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simplify (x+2)/(4x^2+5x+1)*(4x+1)/(x^2-4)

simplify

\frac{x + 2}{4 x ^{2} + 5 x + 1} \cdot \frac{4 x + 1}{x ^{2} - 4}

\frac{1}{( x + 1 ) ( x - 2 )}

Solution steps

\frac{x + 2}{4 x ^{2} + 5 x + 1} \cdot \frac{4 x + 1}{x ^{2} - 4}

Apply the fraction rule:

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

= \frac{( x + 2 ) ( 4 x + 1 )}{( 4 x ^{2} + 5 x + 1 ) ( x ^{2} - 4 )}

Factor

4 x^{2} + 5 x + 1 : (4 x + 1) (x + 1)

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

Cancel the common factor:

4 x + 1

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

Factor

x^{2} - 4 : (x + 2) (x - 2)

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

Cancel the common factor:

x + 2

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

(7 - 3 i) + (x - 2 i)^{2} - (4 i + 2 x^{2})

cot (x) tan (x)

9 x^{2} - 39 x - 30

\frac{x ^{3}}{2} (4 x^{- 1})^{2}

What is (x+2)/(4x^2+5x+1)*(4x+1)/(x^2-4) ?
The solution to (x+2)/(4x^2+5x+1)*(4x+1)/(x^2-4) is 1/((x+1)(x-2))