What is (x+1/2)(x+3/2) ?

The solution to (x+1/2)(x+3/2) is ((2x+1)(2x+3))/4

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simplify (x+1/2)(x+3/2)

simplify

(x + \frac{1}{2}) (x + \frac{3}{2})

\frac{( 2 x + 1 ) ( 2 x + 3 )}{4}

Solution steps

(x + \frac{1}{2}) (x + \frac{3}{2})

Simplify

x + \frac{1}{2} : \frac{2 x + 1}{2}

= \frac{2 x + 1}{2} (x + \frac{3}{2})

Apply the fraction rule:

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

= \frac{( 2 x + 1 ) ( x + \frac{3}{2} )}{2}

Simplify

(2 x + 1) (x + \frac{3}{2}) : \frac{( 2 x + 1 ) ( x \cdot 2 + 3 )}{2}

= \frac{\frac{( 2 x + 1 ) ( x \cdot 2 + 3 )}{2}}{2}

Apply the fraction rule:

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

= \frac{( 2 x + 1 ) ( x \cdot 2 + 3 )}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{( 2 x + 1 ) ( x \cdot 2 + 3 )}{4}

= \frac{( 2 x + 1 ) ( 2 x + 3 )}{4}

(x^{2} + 3 - 2) \cdot (x^{2} + 3 + 2)

(s + \frac{1}{2})^{2}

(1 + 1 - x^{2})^{2}

\frac{x ^{2}}{( x - 3 ) ( x - 5 )}