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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

- 354 + 26

- \frac{1}{2 ^{\frac{4}{3}}}

\frac{5}{2 ^{5}}

\frac{375}{2}

(7^{x})^{2}

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