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

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

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simplify x/2-(x+1)/(4x+2)-1

simplify

\frac{x}{2} - \frac{x + 1}{4 x + 2} - 1

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

Solution steps

\frac{x}{2} - \frac{x + 1}{4 x + 2} - 1

Join

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

Simplify

- 2 (2 x + 1) + x (2 x + 1) - (x + 1) : 2 x^{2} - 4 x - 3

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

\frac{3}{x + 3} - \frac{1}{x - 3}

- \frac{1}{2} \cdot 12 x

\frac{lo g _{7} ( 4 )}{lo g _{7} ( 256 )}

5 x 12 x^{5}

\frac{x ^{3} + y ^{3}}{( x + y ) ^{3}}

What is x/2-(x+1)/(4x+2)-1 ?
The solution to x/2-(x+1)/(4x+2)-1 is (2x^2-4x-3)/(2(2x+1))