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

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

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expand 1/(2x+1)+2/(x-1)

expand

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

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

Solution steps

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

Least Common Multiplier of

2 x + 1, x - 1 : (x - 1) (2 x + 1)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

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

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

Expand

x - 1 + 2 (2 x + 1) : 5 x + 1

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

\frac{( 6 - x ) ^{2}}{4}

a x^{2} + (a + b) x - c

(3 - \frac{e ^{x}}{10})^{2}

((x, y) - (5, 2)) \cdot (- 3, 1)

\frac{11 ( x - 24 )}{2}

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